aThe last breakout session I attended at NCTM's Institute on Reasoning and Sense Making was "Activities That Promote Reasoning and Sense Making in Algebra." This session was led by two math teachers and a principal (and former math teacher) at Adlai E. Stevenson HS in Lincolnshire, IL. John Carter is the principal, Gwen Zimmermann is the department head (of a math department with 43 teachers! - they have 4200 students in their school), and Darshan Jain just finished his first year teaching.
Gwen started off by referencing the 5 Practices book by Peg Smith from my morning keynote. She did briefly go over them as well. Like with the morning breakout session I attended with Bill Thill, I was very actively engaged in the tasks they presented us. Here are my notes of some key points they made:
Learning is a social construction – a lot of learning happens when we talk about the mathematics.
Gwen talked about a “typical” lesson having three phases -
-Launch phase
-Explore phase
-Discuss and summarize
The challenge is to maintain high level of student reasoning throughout task.
U.S. teachers take high cognitive level tasks and reduce to teaching from a procedural perspective (Hiebert research). We tend to tell kids how to do it and/or give too much scaffolding.
We did three activities -
1st Activity: Knots activity (Key Press Discovering Algebra)
Take a piece of rope. Begin tying non-overlapping knots. What might be some questions related to an algebra curriculum that could be asked?
Learning Goal: Approximate and interpret rate of change from graphical and numerical data.
2nd activity: Tile problem **when I have access to the presentation slides, I will link to them so you can see the activity better.
There was a picture of 4 stages of a rectangle constructed with square tiles and an empty space in the middle. The first one was 3 across by 4 wide, with a 1 across by 2 wide empy space in the middle. The second one was 4 by 5 with a 2 by 3 empty space. The third was 5 by 6 with a 3 by 4 empty space, and the fourth was 6 by 7 with a 4 by 5 empty space. We were to answer the following:
How many tiles are needed for a model at stage 5? Stage 11?
Explain how you determined the number need for stage 11.
Determine an expression for the number of tiles in a model of any stage, n.
Make explicit the connection(s) between your expression and the physical model.
This was the first in a series of three tasks that are presented to a beginning algebra class. The second figure is a cross (start with 5 squares, then I think the next was 9, etc.) and the third figure is three-dimensional and is found here (it is the second lesson in the pdf, starting on page 10).
3rd Activity: Rational Functions and Representations
-used with Pre-Calculus students
Students work collaboratively in groups of 3-4.
We had an envelope with 6 different limits, 6 different tables (graphing calculator generated), and 6 different descriptors of what is happening at those specific x-values. We also had a graph to check against. Our tasks were to:
Match the given mini-tables to their corresponding limit representation, then check your paining against the graph provided.
Write the graphical significance of the values shown in the tables and limit representations.
Write the equation of a rational function that may produce the table and graph provided.
At the end of this task, they shared with us that they use this mnemonic device to represent the various representation:
VeGAN TRw (vegan tomorrow)
Verbal description
Graphical representation
Algebraic representation
Numerical representation
Technology as a tool
Real world context
Here are some thoughts they shared with us in closing:
Not all activities that we are going to do are going to be that wide – it’s the questions we ask students that make activities involve reasoning and sense making.
Reasoning and Sense Making in Algebra
• Clear learning goal
• Tasks that supports reasoning and sense making
• Intentional, thoughtful planning and implementation of instructional moves (“planned improvisation”) that actively engage all students in productive mathematical discussions
Like my earlier breakout session, I did not have a lot of notes to share. We spent most of the time doing and discussing the tasks at hand. I found these two sessions very valuable because by the time I was done with them, I felt a little better as far as what I should be pursuing in my planning to promote reasoning and sense making in my classes. Although not many people used the terms "Rich Tasks" or "Rich Problems" often (Bill Thill being the exception), in all reality, those are the types of problems and tasks we should be doing on a much more regular basis.
Am I at a point today to totally do rich problems/tasks in my classroom daily? No. Does it make sense to do these types of tasks everyday. I don't think so. I think there still has to be a place in the classroom for instruction. However, the rich tasks can promote an introduction to a topic and lead students to come up with some conclusions on their own before you tie them together better. I think Henri Picciotto was getting at that in his session and I may have that somewhere in my notes for it - but I am just now making that connection.
I think once I get home and have a little more time to digest this all, I may do one more post on the institute. But I can say that it was worthwhile, I had a lot of good sessions, and I am taking away many things from it.
Sunday, July 31, 2011
NCTM Institute on Reasoning and Sense Making - Rich Tasks in Algebra Work 7/30
We had two breakout sessions on Saturday. The first I attended was “Rich Tasks in Algebra Work: Assessment for Learning in Action” by William Thill from Harvard Westlake. Bill was very up front about what his session was going to be – we would do and analyze a math task, go over what he called the 5 non-negotiable strategies, do some designing work, give and receive some feedback on what we designed, and if there was time, he would share his experience with this task.
His Goals –
• See how analyzing the mathematics of a task influences how you’ll engineer classroom time with your students
• Use “five nonnegotiables” of assessment for learning as a framework to use rich task effectively in your classroom
If you head to the Institute handout website, you will find his handouts, slides, and a couple of other references. Before we got into the task, Bill cited that Park City Mathematics Institute was the most influential experience for him as a mathematics teacher. He also stated that this workshop is about us – not him. The last thing he did before we began was to establish three norms –
• Ask, don’t tell. Share.
• Focus: what can I learn from those next to me? What do I have to offer?
• Keep the right hat on (student or teacher hat)
The particular problem he gave us he called the Trains problem. After working on the task, we looked at the possible mathematical topics as well as possible Mathematical Practices / Habits of Mind it could use. Bill did say that this particular problem could use all eight Standards of Mathematical Practice. He reminded us that tasks don’t teach, teachers teach.
Bill then briefly presented to us the five non-negotiatbles of assessment for learning. They come from an article titled “Classroom Assessment, Minute by Minute, Day by Day” in Educational Leadership (11/2005) by Leahy.
Non Negotiables Assessment for Learning
• Clarify and share learning intentions and criteria for success with students
• Engineer effective classroom discussions, questions and learning tasks
• Provide feedback that moves learners forward
• Activate students as owners of their own learning
• Encourage students to be educational resources for one another
We then went through looking at this task and adapting it to our particular classes. We had to create posters. We put them up and did a gallery walk. Instead of a person staying with the poster, he had us write comments on post-its and left them on the posters. As we were debriefing that process, one participant commented that teachers are a critical group. She had noticed way more negative comments than positive ones. As Bill asked us what we could learn from that comment, we concluded that we should make sure you say something good, before you say something bad.
Of all the sessions I participated in, this was the one I wrote the least amount of notes in. I was a very active participant in this session. It was almost impossible not to be based on how Bill designed the breakout session. I also feel that I got the most out of this session on many levels. It was good to actually see a session with “Rich Task” as part of the title. This is something I have been wanting to delve more into this summer (not that I have gotten there) and I have come to the conclusion that a “Rich Task” has to involve reasoning and sense making. You could almost say that this whole Institute has been focused on the use of “Rich Tasks.” Seeing that now helps make sense of this for me.
Something else that struck me after the fact was in all the other sessions (including the one after this) except for Dan Meyer, the presenters were older, well-experienced teachers. I don't know how many years Bill has taught, but my guess is somewhere between 7 and 10. Seeing a younger teacher doing these kind of activities was powerful for me. As a more experienced teacher (19 years), my natural draw is to see what the younger teachers are doing as being more current and grounded in current math-ed research. It's not that the older, more experienced teachers than I couldn't be up-to-date in research, but my natural tendency is to assume that what they are doing has come from their years of experience. Not new, not fresh. But seeing a younger (than I), less experienced teacher doing these things sends me the signal that this is what is perceived as the current stuff in math ed. In essence, Bill helped validate what everyone else was doing as being the most current thing.
His Goals –
• See how analyzing the mathematics of a task influences how you’ll engineer classroom time with your students
• Use “five nonnegotiables” of assessment for learning as a framework to use rich task effectively in your classroom
If you head to the Institute handout website, you will find his handouts, slides, and a couple of other references. Before we got into the task, Bill cited that Park City Mathematics Institute was the most influential experience for him as a mathematics teacher. He also stated that this workshop is about us – not him. The last thing he did before we began was to establish three norms –
• Ask, don’t tell. Share.
• Focus: what can I learn from those next to me? What do I have to offer?
• Keep the right hat on (student or teacher hat)
The particular problem he gave us he called the Trains problem. After working on the task, we looked at the possible mathematical topics as well as possible Mathematical Practices / Habits of Mind it could use. Bill did say that this particular problem could use all eight Standards of Mathematical Practice. He reminded us that tasks don’t teach, teachers teach.
Bill then briefly presented to us the five non-negotiatbles of assessment for learning. They come from an article titled “Classroom Assessment, Minute by Minute, Day by Day” in Educational Leadership (11/2005) by Leahy.
Non Negotiables Assessment for Learning
• Clarify and share learning intentions and criteria for success with students
• Engineer effective classroom discussions, questions and learning tasks
• Provide feedback that moves learners forward
• Activate students as owners of their own learning
• Encourage students to be educational resources for one another
We then went through looking at this task and adapting it to our particular classes. We had to create posters. We put them up and did a gallery walk. Instead of a person staying with the poster, he had us write comments on post-its and left them on the posters. As we were debriefing that process, one participant commented that teachers are a critical group. She had noticed way more negative comments than positive ones. As Bill asked us what we could learn from that comment, we concluded that we should make sure you say something good, before you say something bad.
Of all the sessions I participated in, this was the one I wrote the least amount of notes in. I was a very active participant in this session. It was almost impossible not to be based on how Bill designed the breakout session. I also feel that I got the most out of this session on many levels. It was good to actually see a session with “Rich Task” as part of the title. This is something I have been wanting to delve more into this summer (not that I have gotten there) and I have come to the conclusion that a “Rich Task” has to involve reasoning and sense making. You could almost say that this whole Institute has been focused on the use of “Rich Tasks.” Seeing that now helps make sense of this for me.
Something else that struck me after the fact was in all the other sessions (including the one after this) except for Dan Meyer, the presenters were older, well-experienced teachers. I don't know how many years Bill has taught, but my guess is somewhere between 7 and 10. Seeing a younger teacher doing these kind of activities was powerful for me. As a more experienced teacher (19 years), my natural draw is to see what the younger teachers are doing as being more current and grounded in current math-ed research. It's not that the older, more experienced teachers than I couldn't be up-to-date in research, but my natural tendency is to assume that what they are doing has come from their years of experience. Not new, not fresh. But seeing a younger (than I), less experienced teacher doing these things sends me the signal that this is what is perceived as the current stuff in math ed. In essence, Bill helped validate what everyone else was doing as being the most current thing.
Saturday, July 30, 2011
NCTM Institute on Reasoning and Sense Making - Implementing Tasks That Promote Reasoning and Sense Making
Saturday morning opens with three keynote speakers for us to choose from. I debated between going to see Tim Kanold, who was talking about PLCs in his session, (Glenn Waddell blogs about it here) and the one I chose, Implementing Tasks that Promote Reasoning and Sense Making with Margaret Smith from The University of Pittsburgh.
She started by stating that selecting a good task is an important first task. We need to select tasks that live up to their potential. Her session is based on her book, Five Practices for Orchestrating Productive Mathematics Discussions – what you need to do before and during the exercise to promote the reasoning and sense making in the exercise. I will note that I had heard a couple of really good recommendations for this book (one in another session) and it was written for teachers. The people who had read it said that it was easy to read and understand and well worth it.
The Five Practices (+)
0. Setting Goals and Selecting Tasks - was added after a discussion with a coach about that it was important to do this before beginning. They had already been calling the rest the Five Practices, so now she refers to them as above.
1. Anticipating
2. Monitoring
3. Selecting
4. Sequencing
5. Connecting
Below I have gone through what information she had posted on the slides (which were helpful) along with parts of an example that she had us work through to see the Five Practices in play.
0. Setting Goals
Involves –
• Identifying what students are to know and understand about mathematics as a result of their engagement in a particular lesson
• Being as specific as possible so as to establish a clear target for instruction that can guide the selection of instructional activities and the use of the five practices
It is supported by –
• Thinking about what student will come to know and understand rather than only on what they will do
• Consulting resources that can help in unpacking big ideas in mathematics
• Working in collaboration with other teachers
Example Goals –
Realize that examples are not enough to show that a claim is always true
Recognize that there are many different ways to prove
0. Selecting Tasks
Involves –
• Identifying a mathematical task that is aligned with the lesson goals
• Making sure the task is rich enough to support a discussion (i.e. a cognitively challenging mathematical task)
It is supported by –
• Setting a clear and explicit goal for learning
• Collaboration
Example task – Prove that the sum of two odd numbers is always even
1. Anticipating
Likely student responses to mathematical problems
Involves considering –
• The array of strategies that students might use to approach or solve a challenging mathematical task
• How to respond to what students produce
• Which strategies will be most useful in addressing the mathematics to be learned
It is supported by –
• Doing the problem in as many ways as possible (YOU doing the problem)
• Doing so with other teachers
• Drawing on relevant research
• Documenting student responses from year to year
Examples –
Thought students might draw a picture, build a model, create a logical argument, use algebra
Thought students might use examples and not know what else to do
Thought students might use the same variable in the representation of each odd number
2. Monitoring
Students’ actual responses during independent work
Involves –
• Circulating while students work on the problem and watching and listening
• Recording interpretations, strategies, and points of confusing
• Asking questions to get students back “on track” or to advance their understanding
It is supported by –
• Anticipating student responses beforehand
• Using a recording sheet (We had a packet with this in it. It had headings of Strategy, Who and What, and Order.)
• On the recording sheet – under strategy, fill in what you came up with in the anticipating step
The recording sheet serves as a record of who’s doing what and helps you to decide what to share with the class. It also helps keep track of strategies that students are using and you can use that data to help form groups.Also provides a historical record for you to look at the next time you do this lesson.
Examples –
Teacher asked a lot of questions to understand what they were doing, to help students to access relevant knowledge, and to suggest an avenue to pursue. Teacher left the groups with ideas to pursue and gave them the space and time to pursue them. Teacher also suggested resources that would help students make progress.
Teacher didn’t tell students what to do or how to do it.
3. Selecting
Student responses to feature during discussion
Involves –
• Choosing particular students to present because of the mathematics available in their responses
• Making sure that over time all students are seen as authors of mathematical ideas and have the opportunity to demonstrate competence
• Gaining some control over the content of the discussion (no more “who wants to present next”)
It is supported by –
• Anticipating and monitoring
• Planning in advance which types of responses to select
4. Sequencing
Student responses during the discussion
Involves –
• Purposefully ordering presentations so as to make the mathematics accessible to all students
• Building a mathematically coherent story line
(don’t start with the most abstract solution first – you need to build to it)
It is supported by –
• Anticipating, monitoring, and selecting
Example – went from concrete to abstract, left the groups with issues for the end
5. Connecting
Student responses during the discussion
Involves –
• Encouraging student to make mathematical connections between different student responses
• Making the key mathematical ideas that are the focus of the lesson salient
It is supported by –
• Anticipating, monitoring, selecting, and sequencing
• During planning, considering how students might be prompted to recognize mathematical relationships between responses
Examples –
All of the solutions were connected to each other and key ideas of number theory (e.g. an even number is divisible by 2, can be represented algebraically)
Teacher encouraged student to question each other. Teacher asked students to relate their work to the work of other students in the class. Teacher created homework that requires students to make sense of the arguments and reasoning of others. Teacher established a classroom climate in which students feel they can contribute.
What’s the point –
Good tasks are a critical starting point for developing student capacity to reason, but tasks alone are not enough.
I really liked this session. I felt like I left with a better understanding of how to promote some discussion in my classroom. I have a lot to learn about that yet, and I will definitely be purchasing the book she has co-written on the subject, especially after hearing good recommendations from others who have read it.
She started by stating that selecting a good task is an important first task. We need to select tasks that live up to their potential. Her session is based on her book, Five Practices for Orchestrating Productive Mathematics Discussions – what you need to do before and during the exercise to promote the reasoning and sense making in the exercise. I will note that I had heard a couple of really good recommendations for this book (one in another session) and it was written for teachers. The people who had read it said that it was easy to read and understand and well worth it.
The Five Practices (+)
0. Setting Goals and Selecting Tasks - was added after a discussion with a coach about that it was important to do this before beginning. They had already been calling the rest the Five Practices, so now she refers to them as above.
1. Anticipating
2. Monitoring
3. Selecting
4. Sequencing
5. Connecting
Below I have gone through what information she had posted on the slides (which were helpful) along with parts of an example that she had us work through to see the Five Practices in play.
0. Setting Goals
Involves –
• Identifying what students are to know and understand about mathematics as a result of their engagement in a particular lesson
• Being as specific as possible so as to establish a clear target for instruction that can guide the selection of instructional activities and the use of the five practices
It is supported by –
• Thinking about what student will come to know and understand rather than only on what they will do
• Consulting resources that can help in unpacking big ideas in mathematics
• Working in collaboration with other teachers
Example Goals –
Realize that examples are not enough to show that a claim is always true
Recognize that there are many different ways to prove
0. Selecting Tasks
Involves –
• Identifying a mathematical task that is aligned with the lesson goals
• Making sure the task is rich enough to support a discussion (i.e. a cognitively challenging mathematical task)
It is supported by –
• Setting a clear and explicit goal for learning
• Collaboration
Example task – Prove that the sum of two odd numbers is always even
1. Anticipating
Likely student responses to mathematical problems
Involves considering –
• The array of strategies that students might use to approach or solve a challenging mathematical task
• How to respond to what students produce
• Which strategies will be most useful in addressing the mathematics to be learned
It is supported by –
• Doing the problem in as many ways as possible (YOU doing the problem)
• Doing so with other teachers
• Drawing on relevant research
• Documenting student responses from year to year
Examples –
Thought students might draw a picture, build a model, create a logical argument, use algebra
Thought students might use examples and not know what else to do
Thought students might use the same variable in the representation of each odd number
2. Monitoring
Students’ actual responses during independent work
Involves –
• Circulating while students work on the problem and watching and listening
• Recording interpretations, strategies, and points of confusing
• Asking questions to get students back “on track” or to advance their understanding
It is supported by –
• Anticipating student responses beforehand
• Using a recording sheet (We had a packet with this in it. It had headings of Strategy, Who and What, and Order.)
• On the recording sheet – under strategy, fill in what you came up with in the anticipating step
The recording sheet serves as a record of who’s doing what and helps you to decide what to share with the class. It also helps keep track of strategies that students are using and you can use that data to help form groups.Also provides a historical record for you to look at the next time you do this lesson.
Examples –
Teacher asked a lot of questions to understand what they were doing, to help students to access relevant knowledge, and to suggest an avenue to pursue. Teacher left the groups with ideas to pursue and gave them the space and time to pursue them. Teacher also suggested resources that would help students make progress.
Teacher didn’t tell students what to do or how to do it.
3. Selecting
Student responses to feature during discussion
Involves –
• Choosing particular students to present because of the mathematics available in their responses
• Making sure that over time all students are seen as authors of mathematical ideas and have the opportunity to demonstrate competence
• Gaining some control over the content of the discussion (no more “who wants to present next”)
It is supported by –
• Anticipating and monitoring
• Planning in advance which types of responses to select
4. Sequencing
Student responses during the discussion
Involves –
• Purposefully ordering presentations so as to make the mathematics accessible to all students
• Building a mathematically coherent story line
(don’t start with the most abstract solution first – you need to build to it)
It is supported by –
• Anticipating, monitoring, and selecting
Example – went from concrete to abstract, left the groups with issues for the end
5. Connecting
Student responses during the discussion
Involves –
• Encouraging student to make mathematical connections between different student responses
• Making the key mathematical ideas that are the focus of the lesson salient
It is supported by –
• Anticipating, monitoring, selecting, and sequencing
• During planning, considering how students might be prompted to recognize mathematical relationships between responses
Examples –
All of the solutions were connected to each other and key ideas of number theory (e.g. an even number is divisible by 2, can be represented algebraically)
Teacher encouraged student to question each other. Teacher asked students to relate their work to the work of other students in the class. Teacher created homework that requires students to make sense of the arguments and reasoning of others. Teacher established a classroom climate in which students feel they can contribute.
What’s the point –
Good tasks are a critical starting point for developing student capacity to reason, but tasks alone are not enough.
I really liked this session. I felt like I left with a better understanding of how to promote some discussion in my classroom. I have a lot to learn about that yet, and I will definitely be purchasing the book she has co-written on the subject, especially after hearing good recommendations from others who have read it.
NCTM Institute on Reasoning and Sense Making - Making Sense in Algebra 2 7/29
The last breakout workshop I attended on Friday was “Making Sense in Algebra 2” led by Henri Picciotto from The Urban School of San Francisco. All handouts are available on his website (www.MathEducationPage.org/alg-2).
By the time I got to this session, I was hitting the mid-afternoon doldrums that you especially get when you have been at a conference all day and you’re not used to all that learning. This session was full and they did not have enough handouts. They were good and eventually got them to us all. I ended up at a seat on the side, so I wasn’t able to participate in the activities that used manipulatives.
-levels the playing field
-enhances calculator/Fathom/spreadsheet fluency
-formulas encapsulate understanding, are not an obstacle to it, or a substitute for it
-introduces convergence, divergence, limits
-makes arithmetic and geometric sequences look easy!
(starts with something more difficult and makes things look easier)
Making sense – concepts first (not notation, not terminology)
The activity involved finding the exponent in the expression 10 to a power (it’s called Super Scientific Notation). This activity gives meaning to logs, emphasizing that logs are exponents and helps to justify log rules. Henri did note that students do panic when intro notation and terminology – but remind them of this anchor activity and it eases their panic.
Application of geometry
By the time I got to this session, I was hitting the mid-afternoon doldrums that you especially get when you have been at a conference all day and you’re not used to all that learning. This session was full and they did not have enough handouts. They were good and eventually got them to us all. I ended up at a seat on the side, so I wasn’t able to participate in the activities that used manipulatives.
His solution for Making Sense in Algebra 2:
- Escape from the textbook!
- Choose depth over breadth
- Keep tweaking the course
- Collaboration makes it possible - His department meets every week and continues to communicate.
We spent most of the rest of the session working through problems. Some of the activities involved using algebra tiles and other manipulatives. With each of the problems, he concluded with a point about making sense. Those points are:
Making Sense – Start with a Big Question:
Starting with iteration…-levels the playing field
-enhances calculator/Fathom/spreadsheet fluency
-formulas encapsulate understanding, are not an obstacle to it, or a substitute for it
-introduces convergence, divergence, limits
-makes arithmetic and geometric sequences look easy!
(starts with something more difficult and makes things look easier)
Making sense – use manipulatives as an exploration, reflection, and discussion environment
Making Sense – use real “real world” connections
-hands-on experiments motivate the concepts.Making sense – concepts first (not notation, not terminology)
The activity involved finding the exponent in the expression 10 to a power (it’s called Super Scientific Notation). This activity gives meaning to logs, emphasizing that logs are exponents and helps to justify log rules. Henri did note that students do panic when intro notation and terminology – but remind them of this anchor activity and it eases their panic.
Making sense – reason about numbers
Connection to artApplication of geometry
At the end, Henri gave us his strategies for sense making:
- Do fewer topics in more depth
- Sequence them strategically
- Start units with memorable anchor problems
- Incorporate manipulative and electronic tools
- Concepts first
- Formulas, notation, terminology – handle with care!
- Navigate between multiple representations
- Do not skimp on visual, geometric, and hands-on approaches
I struggled somewhat with this session. After having spent time looking at what Dan Meyer was presenting and working on incorporating media and a “wow!” factor to it all, this seemed somewhat duller to me. However, upon further reflection and discussion, I am seeing that one cannot do that type of thing all of the time. It loses its “shiny” nature to students. If you do the same thing all the time, even if it’s wonderful, it will lose some of its effectiveness. I think there is some merit with what Henri presented. I’m still trying to figure out how to make it all work for me.
NCTM Institute on Reasoning and Sense Making - It All Starts with the Tasks 7/29
Friday afternoon, we had three keynote presentations to choose from. I chose to attend “Reasoning and Sense Making: It All Starts with the Tasks,” which was a presentation by W. Gary Martin from Auburn University and Eric Robinson from Ithaca College. Gary has worked on Appendix A of the Common Core State Standards, the NCTM Principles and Standards for School Mathematics, and the High School Focus on Reasoning and Sense Making book that we were all given. He is on the task writing group that Eric Robinson chairs. Both gentlemen have a lot of experience writing tasks, including many we are seeing here at the Institute.
Mainly here, I have my notes – points they made that I found interesting to think about. I am leaving many of these in “note” form because I had written them as points to consider.
Gary spoke first, asking us to consider a problem that asks us to factor a trinomial. He asked us to look at two questions –
What mathematical thinking are you likely to get from your students? Recall, either they know what to do or not.
What kind of mathematical thinking would we like to get? The reasoning and sense making – the thinking.
In the High School Focus on Reasoning and Sense Making book, there are four reasoning habits given:
What makes a task use reasoning and sense making?
-The math might be useful in solving the problem.
-It makes sense to do this math to answer an interesting question.
-You understand how the particular mathematical content and mathematical reasoning relate to the problem at hand (or contributes to a deeper understanding of the mathematics itself)
You can make (mathematical sense) sense of your solutions to others.
-knowledge of students’ understandings, interests, and experiences
-knowledge of the range of ways that diverse students learn mathematics
-Vary the task
-Provide scaffolding
-Provide a task with multiple entry levels and appropriate teacher support.
-Only calling on students who you think know the answer
-Body language (similar to what Dan had talked about in his keynote)
Eric Robinson cited Questioning Our Pattern of Questioning (Herbell-Eisenmann & Breyfogle, 2006) –
Many teachers do either Imitation-Response-Feedback type questioning or funneling (keep narrowing your questions to get where you want to be). They proposed an alternative pattern – Focusing, where the teacher listens to the students’ responses and guides them based on what the students are thinking rather than what the teacher thinks is the best solution.
Benefits:
It allows the teacher to understand what the students are thinking
nctm.org/hsfocus
Illuminations.nctm.org
Insidemathematics.org
NSF-funded currciula – http://www.imp.org/, www.wmich.edu/comp/, www.montana.edu/wwwsimms, www.comap.com/mmow/, http://www.cmeproject.edc.org/ - I have to check the slide once it's posted to make sure I have the un-linked ones correct.
Illustrative Mathematics mentioned this morning
Purplemath
Heinemann – search tasks **this was audience mentioned, but I'm not finding it.
Mathematics Assessment Project
Calculation Nation
Math Forum
Gary closed by going back to the original problem – factor x^2 – 7x + 12. Suggestions to change it to involve more reasoning and sense making:
Mainly here, I have my notes – points they made that I found interesting to think about. I am leaving many of these in “note” form because I had written them as points to consider.
Gary spoke first, asking us to consider a problem that asks us to factor a trinomial. He asked us to look at two questions –
What mathematical thinking are you likely to get from your students? Recall, either they know what to do or not.
What kind of mathematical thinking would we like to get? The reasoning and sense making – the thinking.
In the High School Focus on Reasoning and Sense Making book, there are four reasoning habits given:
- Analyzing a problem
- Implementing a strategy
- Seeking and using connections
- Reflecting on a solution to a problem
It’s more about the nature of what students are doing in the classroom – are they just mimicking or are they thinking?
What makes a task use reasoning and sense making?
- multiple points of entry
- trial and error – why is something right, why is something wrong
- non-routine
- more than one answer
- discussion was helpful
- simple to get into – not that elaborate
-The math might be useful in solving the problem.
-It makes sense to do this math to answer an interesting question.
The mathematics you are doing makes sense.
-You understand how the mathematics works.-You understand how the particular mathematical content and mathematical reasoning relate to the problem at hand (or contributes to a deeper understanding of the mathematics itself)
You can make (mathematical sense) sense of your solutions to others.
The teacher of mathematics should pose tasks that are based on –
-sound and significant mathematics-knowledge of students’ understandings, interests, and experiences
-knowledge of the range of ways that diverse students learn mathematics
-Vary the task
-Provide scaffolding
-Provide a task with multiple entry levels and appropriate teacher support.
You can also minimize the reasoning and sense making that students might experience in a supposedly good task by:
-Discussing your answer before the students have had a chance to think about the problem for themselves.-Only calling on students who you think know the answer
-Body language (similar to what Dan had talked about in his keynote)
Eric Robinson cited Questioning Our Pattern of Questioning (Herbell-Eisenmann & Breyfogle, 2006) –
Many teachers do either Imitation-Response-Feedback type questioning or funneling (keep narrowing your questions to get where you want to be). They proposed an alternative pattern – Focusing, where the teacher listens to the students’ responses and guides them based on what the students are thinking rather than what the teacher thinks is the best solution.
Benefits:
It allows the teacher to understand what the students are thinking
- It provides students an opportunity to clarify their thinking well enough to communicate to the class
- It provides members of the class opportunities to encounter different approaches to the problem
nctm.org/hsfocus
Illuminations.nctm.org
Insidemathematics.org
NSF-funded currciula – http://www.imp.org/, www.wmich.edu/comp/, www.montana.edu/wwwsimms, www.comap.com/mmow/, http://www.cmeproject.edc.org/ - I have to check the slide once it's posted to make sure I have the un-linked ones correct.
Illustrative Mathematics mentioned this morning
Purplemath
Heinemann – search tasks **this was audience mentioned, but I'm not finding it.
Mathematics Assessment Project
Calculation Nation
Math Forum
They also suggested that you can adapt an existing task to better meet the needs of your students. This can be done by changing the content, adjusting the mathematical level (without adjusting the necessity of reasoning and sense making), or even going to the point of creating a new task.
Gary closed by going back to the original problem – factor x^2 – 7x + 12. Suggestions to change it to involve more reasoning and sense making:
- Maybe put it in the context of the area of a rectangle.
- Tiles
- The easy fix he proposed was to change it to: Find coefficients for x so that you can factor the trinomial x^2 - ?x + 12
Friday, July 29, 2011
NCTM Institute on Reasoning and Sense Making - Capturing Perplexity Breakout Session (Dan Meyer) 7/29
I should begin by laying out the following things for the reader -
This was an hour and fifteen minute breakout session with Dan Meyer titled Capturing Perplexity. Dan delivered the opening keynote yesterday. Within one minute (I am not kidding) of the dismissal from the Panel Discussion, this session was standing room only. NCTM personnel kicked anyone out without a seat, but not before announcing that Dan had graciously agreed to do this session again in the afternoon in place of a session that had to be cancelled. He later tweeted that the afternoon session was almost full in spite of it only being announced by people on twitter and word of mouth.
My notes are a little more sketchy here at times because I was being an active participant in the session. I did really like that Dan had us engaged and we weren't all looking at packets of problems as I am accustomed to at a workshop.
Dan began with a worksheet involving census data that a teacher had emailed him that used U.S. census data. There were two columns – one for your county, one for neighboring county. It was three pages of questions (2 of them pretty full of stuff) and the verbalization of the question is on the last line of page 3. He then proceeds to tell us that the biggest thing to do is to get the verbalization away from the end of the problem and move it to the beginning. Then do the abstraction – start looking for what information you need.
The session was broken down into three parts.
Part One: Look at Textbook Problems and Make Them Over
He put 4 problems in front of us and we were to determine “where’s the hook?” and "what's the hook?" I'm not going to bore you with all the details. After all, I really think that you need to go see him and experience all the Dan Meyer goodness in person. So I can't tell you everything or it will be spoiled for you when you have the opportunity yourself. Here are some of the issues/bad points of these problems:
"Let’s word these things like human beings." The problems aren't worded well and in some cases they are downright awkwardly worded. In one problem I think he counted 15 words to the question that we/he worded in 4 words.
In the textbook world, you get the info before the question. Not that way in the real world.
Don’t have the abstraction already on the image – doesn’t let kids wonder.
Keep in mind that the information you are presenting is the starting point, not the ending point.
Part Two: Look at Video and the Internet
**Note - You can find the slides and videos referenced here. **
Dan shares with us that the first year he taught at the bottom of the warm ups, he would have some fact. At the end of the year, it dawned on him that he had it all wrong - it didn't engage the students. So the second year, he flipped it around into a question. Instead of telling students that Oman is the only country that starts with "O," he would put on the warm up "What is the only country that starts with 'O'?" Or "How many letters in the Hawaiian alpabet?" Or "What is the longest one-syllable word?"1 If we bring in the image and look at it with all the information given to them and move on, this is equivalent to giving the students the fun fact. Students don't really engage with the material. When you take an impage and use it for motivation of the question, students engage with the material and all sorts of great things happen.
We then proceed to work with a graph (see Everybody Flushes on the referenced website). We had a great discussion about it. We talked about how to work with the graph since it wasn't our original graph - and this was really great because Dan modified it right there and talked about what to do. Now, granted, people who are more comfortable with technology would have recognized that he created some white rectangles to cover the labels, but if you haven't ever done this before, it is powerful to see it done. I thought this was great. This way, you can have two graphs - the original one that you captured from the website and the one you obscured. The idea here is to look at what is interesting, whatever it is that gets your adrenaline going with the picture or video, obscure it and make that the question you are going for. Then you can reveal the information to answer the question. Keep in mind that there are different levels of obscuring you can use depending on your students. Seeing this in action - watching someone go through the process helped clarify this even more for me. In addition, it has given me even more confidence to proceed on my own. Now to find those things to use...
Part Three: Turn Your Own Lives Into Mathematical Inspiration
A lot of this gets to the heart of the #anyqs challenge - find one photo or one minute or less of video and ask "any questions?" Your video or photo should strongly evoke the same question from your audience.
We finished the session by looking at several photos and videos and trying to decide "What makes a good photo or video?" You can go to the earlier referenced website Dan set up to see the photos and videos. Most of these I had seen as they came through #anyqs but it was still a valuable exercise to ask yourself what question you have and rate how strongly you want to know the answer to the question. Here was the list we generated as a group:
Snickers bar video: (most perplexing of the group)
1 12 letters; screeched or strengths
This was an hour and fifteen minute breakout session with Dan Meyer titled Capturing Perplexity. Dan delivered the opening keynote yesterday. Within one minute (I am not kidding) of the dismissal from the Panel Discussion, this session was standing room only. NCTM personnel kicked anyone out without a seat, but not before announcing that Dan had graciously agreed to do this session again in the afternoon in place of a session that had to be cancelled. He later tweeted that the afternoon session was almost full in spite of it only being announced by people on twitter and word of mouth.
My notes are a little more sketchy here at times because I was being an active participant in the session. I did really like that Dan had us engaged and we weren't all looking at packets of problems as I am accustomed to at a workshop.
Dan began with a worksheet involving census data that a teacher had emailed him that used U.S. census data. There were two columns – one for your county, one for neighboring county. It was three pages of questions (2 of them pretty full of stuff) and the verbalization of the question is on the last line of page 3. He then proceeds to tell us that the biggest thing to do is to get the verbalization away from the end of the problem and move it to the beginning. Then do the abstraction – start looking for what information you need.
The session was broken down into three parts.
Part One: Look at Textbook Problems and Make Them Over
He put 4 problems in front of us and we were to determine “where’s the hook?” and "what's the hook?" I'm not going to bore you with all the details. After all, I really think that you need to go see him and experience all the Dan Meyer goodness in person. So I can't tell you everything or it will be spoiled for you when you have the opportunity yourself. Here are some of the issues/bad points of these problems:
"Let’s word these things like human beings." The problems aren't worded well and in some cases they are downright awkwardly worded. In one problem I think he counted 15 words to the question that we/he worded in 4 words.
In the textbook world, you get the info before the question. Not that way in the real world.
Once you have the hook, students have to know who we’re talking about. We want a visual that asks the question and lets us do work on it/with it.
Don’t have the abstraction already on the image – doesn’t let kids wonder.
Keep in mind that the information you are presenting is the starting point, not the ending point.
Part Two: Look at Video and the Internet
**Note - You can find the slides and videos referenced here. **
Dan shares with us that the first year he taught at the bottom of the warm ups, he would have some fact. At the end of the year, it dawned on him that he had it all wrong - it didn't engage the students. So the second year, he flipped it around into a question. Instead of telling students that Oman is the only country that starts with "O," he would put on the warm up "What is the only country that starts with 'O'?" Or "How many letters in the Hawaiian alpabet?" Or "What is the longest one-syllable word?"1 If we bring in the image and look at it with all the information given to them and move on, this is equivalent to giving the students the fun fact. Students don't really engage with the material. When you take an impage and use it for motivation of the question, students engage with the material and all sorts of great things happen.
We then proceed to work with a graph (see Everybody Flushes on the referenced website). We had a great discussion about it. We talked about how to work with the graph since it wasn't our original graph - and this was really great because Dan modified it right there and talked about what to do. Now, granted, people who are more comfortable with technology would have recognized that he created some white rectangles to cover the labels, but if you haven't ever done this before, it is powerful to see it done. I thought this was great. This way, you can have two graphs - the original one that you captured from the website and the one you obscured. The idea here is to look at what is interesting, whatever it is that gets your adrenaline going with the picture or video, obscure it and make that the question you are going for. Then you can reveal the information to answer the question. Keep in mind that there are different levels of obscuring you can use depending on your students. Seeing this in action - watching someone go through the process helped clarify this even more for me. In addition, it has given me even more confidence to proceed on my own. Now to find those things to use...
Part Three: Turn Your Own Lives Into Mathematical Inspiration
A lot of this gets to the heart of the #anyqs challenge - find one photo or one minute or less of video and ask "any questions?" Your video or photo should strongly evoke the same question from your audience.
We finished the session by looking at several photos and videos and trying to decide "What makes a good photo or video?" You can go to the earlier referenced website Dan set up to see the photos and videos. Most of these I had seen as they came through #anyqs but it was still a valuable exercise to ask yourself what question you have and rate how strongly you want to know the answer to the question. Here was the list we generated as a group:
What makes a perplexing photo / video?
Snickers bar video: (most perplexing of the group)
- drama
- music
- you can relate to it
- knew it was going to be a math question – suspense
- aesthetic video quality
We also talked about the two faucet examples that Dan had gotten in Grand Forks and why we felt one was better than the other. This also helped to see what *not* to do when creating these images.
This session was everything I hoped, and then some. Probably the biggest thing for me personally to take away from it is the confidence that I can do this. I truly feel armed and ready for the next image or video that strikes me as relevant to the mathematics we encounter in my classes. It has also encouraged me to stop and think more as I plan - what would be an engaging "real world" example to illustrate what I want students to learn and then see what I can find and create. Having been a "traditional" teacher for my 19 years of teaching to this point, this is huge for me. I can't say that I have felt this confident about working through the three acts/four tasks that Dan has brought to our attention until today. I feel empowered and ready to tackle this even though this represents a radical shift in my classroom. Having the opportunity to see the process first hand and work through the key questions made it very clear for me. I think it's like many things we encounter in life - reading it is good, but experiencing it is so much better. If you have not had the opportunity to see Dan Meyer present and/or participate in a workshop he is doing, find one and go. It should be on every math teacher's "Math Teacher Bucket List" - see Dan Meyer present. I am confident that you will not regret it.
1 12 letters; screeched or strengths
NCTM Institute on Reasoning and Sense Making - Panel Discussion 7/29
Here are my notes from this morning's panel disucssion, which was titled "How Do I Use Standards to Support Teaching for Reasoning and Sense Making? Students’ Reasoning and Sense Making as the Focus of the High School Classroom in the Era of the Common Core State Standards in Mathematics." The panelists were Ed Dickey (University of South Carolina), moderator, Gail Burrill (Michigan State University, NCTM past president), Jeremy Kilpatrick (University of Georgia), and William McCallum (University of Arizona).
First, each of the panelists were given time to present on the topic. Then Ed posed two questions to the panel, which he had emailed to them in advance. Finally, there was some time for audience questions.
First up was Gail Burrell. Some of the main points I got from her presentation:
Jeremy -
A MC Question:
In pyramids ABCD and EFGHI shown above, all faces except base FHGI are equilateral triangles of equal size. If face ABC were placed on face EFG so that the vertices of the triangles coincide, how many exposed faces would the resulting solid have?
5 – 6 – 7 – 8 – 9 (7 – testmakers thought was correct)
The correct answer is 5 (found by a 17 year old student at the time). Tests had to be rescored and credit given for 5 or 7.
If only 5 had been keyed correct, the item would have lost almost all of its worth for measurement.
Gail –
Park City Math Institute is the most effective model she knows.
We expect teachers to continue to do mathematics. Teachers are thinking about the practice of teaching. We have to look at what works as well as what doesn’t work. Teachers have to work together to become resources for their colleagues.
What are the advantages and disadvantages of the two models in Common Core State Standards?
Gail – we looked at the textbooks to see what they are delivering for kids. Would not pick a side. Wants to know what the materials provide.
Jeremy – Integrated is in general a better curriculum. If you are going to make a switch, you have to prepare teachers for the switch.
Professional Teaching Standards NCTM 1991
PCMI Website at Math Forum – materials for those workshops.
Commoncoretools.wordpress.com
First, each of the panelists were given time to present on the topic. Then Ed posed two questions to the panel, which he had emailed to them in advance. Finally, there was some time for audience questions.
First up was Gail Burrell. Some of the main points I got from her presentation:
- What are standards? Are they the curriculum? Or are they?
- Kids can think and reason, but we don’t let them do that. It’s pretty hard to think and reason with a typical list of problems in a textbook.
- Students must learn mathematics with understanding, actively building new knowledge from experience and previous knowledge.
- How students should work – Standards for Mathematical Practices. These are the kinds of ways we want kids to engage in mathematics.
- Thinking and reasoning depends on the types of questions we ask. We should be asking questions like “what is the meaning,” “what are the characteristics,” “how are they different,” etc.
- Ask the types of questions that get at what kids think.
- You need to have opportunities for discussion in the mathematics classroom.
- Think about the math talk in my classroom. Who talks more – me, one or two students, or most of the class? How much do I talk? How much do the students talk? Do my statements of questions encourage thinking and reasoning? Do I spend the time necessary to let students think and reason?
Next we heard from Jeremy Kilpatrick. Points he made that caught my attention:
- The Content Standards – Process Standards Dilemma: Content Standards are the ones we usually talk about. Test items group nicely by content but not by process standards. Also content standards are the “coin of the realm” in discussions of curriculum and standards.
- How do we tie the process standards to specific content is the pressing problem for teachers with Common Core State Standards. (e.g. Reason about and solve one-variable equations and inequalities – grade 6)
- It’s easy to do the content thing. It’s hard to do the process thing.
- How do we do this? Teaching mathematics through problem solving.
- George Polya – Read Mathematical Discovery (out of print) and The Stanford Mathematics Problem Book (back in print now)
- Polya’s important maxims about problem solving: 1) Learn problem solving by imitation and practice and 2) Reflect on one’s practice (we have to think about what we have done)
- Sarah Donaldson dissertation – Teaching through problem solving: Practices of four high school mathematics teachers. She watched and interviewed 4 teachers who use problem solving in their classroom on a regular basis. Common practices of the 4 teachers:
They all taught problem-solving strategies
Modeling problem solving (pretend you haven’t seen the problem before, model the act of problem solving)
Limiting teaching input
Promoting metacognition (solving the problem and then talking about yourself solving the problem – think about what you are doing, “watch yourself”)
Highlighting multiple solutions (push for other ways to solve the problem)
Last was William McCallum. If you are not aware, he was part of the committee who wrote the Common Core State Standards, so many of his points had to deal with the CCSS themselves.Important points to me:
- Teachers often don’t support reasoning and sense making
- He starts with a Grecian Urn – has form and shape and many fine details. Write standards for them, you end up with a pile of rubble.
- Does the text capture the structure of the subject? All the pieces are there, but you can’t see the structure.
- The structure is the standards. Process comes in navigating the standards.
- How to navigate structure, how to proceed structure (Standards for Mathematical Practice)
- The focus and coherence of the Standards for Mathematical Content are part of the standards.
- • The individual standards are part of the standards
- • They fit together into clusters, with descriptive headings that are part of the standards.
- • Clusters fit together into domains, whose names and arrangement are part of the standards.
- • In high school, domains are arranged into conceptual categories, which are part of the standards.
- Students need to see expressions as numbers.
- Think about the standards as not just the individual standards, but also the whole structure.
- http://www.illustrativemathematics.org/ – allows you to look at the Common Core State Standards from grade to grade.
- When you look at the Grecian urn – you look at the whole picture, then look at the details. We should be doing the same idea with the standards.
Then Ed Dickey asked the following questions for the panel:
1) As teachers of mathematics, how do you assess reasoning and sense making?Jeremy -
A MC Question:
In pyramids ABCD and EFGHI shown above, all faces except base FHGI are equilateral triangles of equal size. If face ABC were placed on face EFG so that the vertices of the triangles coincide, how many exposed faces would the resulting solid have?
5 – 6 – 7 – 8 – 9 (7 – testmakers thought was correct)
This is #44 on the 1981 PSAT.
The correct answer is 5 (found by a 17 year old student at the time). Tests had to be rescored and credit given for 5 or 7.
If only 5 had been keyed correct, the item would have lost almost all of its worth for measurement.
2) Will the adoption of the Common Core State Standards we have a broad national models of what to teach. What about Professional Development?
Gail –
Park City Math Institute is the most effective model she knows.
We expect teachers to continue to do mathematics. Teachers are thinking about the practice of teaching. We have to look at what works as well as what doesn’t work. Teachers have to work together to become resources for their colleagues.
Finally we conlcuded with audience questions –
What are the advantages and disadvantages of the two models in Common Core State Standards?
Gail – we looked at the textbooks to see what they are delivering for kids. Would not pick a side. Wants to know what the materials provide.
Jeremy – Integrated is in general a better curriculum. If you are going to make a switch, you have to prepare teachers for the switch.
William agreeed with Gail.
We want a greater and deeper understanding of mathematics in elementary and middle school years. With the way the current system is, we have a mile wide and inch deep curriculum. Is there some thought of instead of age progression to do content progression?
Jeremy – some of the best Professional Development out there is taking a look at the progression of the standards. You have to decide what to emphasize.
Gail – HS teachers need to look at what is happening in the Middle Grades. (a lot of what we do in 9th grade now is there) Assumption is that we are not going to back and reteach. Have to find a way to build support when students fall behind in the early elementary grades. District wide intervention needed (like in reading).
Paul Foerester – we are not here to cover material, we are here to uncover the material. When we come to something students should know, he would say “You recall… (whatever it is).” and would expect students to recall whatever it was after that without him telling them.
Resources to look at:
Professional Teaching Standards NCTM 1991
PCMI Website at Math Forum – materials for those workshops.
Commoncoretools.wordpress.com
Overall, I thought there were some interesting points in this session. No real "Wow!" moments for me, but I think the session was good in making clear why the Standards of Mathematical Practice is important.
Thursday, July 28, 2011
NCTM Institute on Reasoning and Sense Making - Dan Meyer Keynote
I am at the NCTM Institute about Infusing Reasoning and Sense Making into the Classroom in Orlando this week. I have been looking forward to this workshop since I heard about it at the NCTM National Conference at the end of April, especially when I read that Dan Meyer was the opening keynote speaker. I have to say I was not disappointed and was actually very pleased. If you ever have the chance to see Dan present, go. Well worth the price of admission.
Rather than sum up everything he talked about, I will hit some of the high points. Some what he presented are parts of blog posts he has done this summer.
Dan opened with the story of his favorite horse, Clever Hans. If you are not familiar, Clever Hans is the horse around the turn of the century who could predict the answer of any mathematical question. When researchers tried to figure out what was so special about Clever Hans, they figured out that if the person who questioned him didn't know the answer or wasn't visible to Clever Hans, he would miss the question. Basically, what Dan is getting at here is something most of us do as teachers is like what Clever Hans' questioners did - we give away whether a student is correct by any one of a number of visual or verbal cues. Ultimately, we are creating a bunch of Clever Hans' - students who can figure out if they're right, instead of Smart Hans', who can reason and make sense of what they are doing mathematically and find the correct answer on their own.
When Dan talked about the Clever Hans story and got to his point, I felt very convicted. I do this too. I need to get away from that and work on being less helpful. In a later discussion at my strand session (I'm in Intermediate Algebra), I was sitting at a table with Hank Kepner (past NCTM president). He was talking about a similar thing in his classroom when he taught. I asked him, what do you do when the student presents you with a correct solution. His response was to ask them why it was correct. He wants his students to be able to defend their answer and know why the answer is good - the process is more important than the answer. Between these two things, I realize that I really need to learn about questioning and how to be more effective in the classroom. Less Clever Hans trainer and more a guide. Need to figure that out, and soon.
Enough chasing rabbits for now and back to Dan. He then went through a bit about curriculum and talked about application problems - problems that are practical (when am I ever going to use this?) and/or explanatory (even though we aren't using math, math is using us). For practical, he uses the example of helping his parents figure out whether it was cheaper to drive and park at the SF airport or drive part-way to (I forget where), park and take the shuttle. For explanatory, he uses the basketball problem.
Another point Dan made was our textbooks are set up to connect problems to previously worked examples – our textbooks even tell us where to find the examples. Too fill-in-the-blanky. Don’t reduce math to filling in blanks and working fixed examples. This is something else I am guilty of. Give the example and problems are similar to them. I had already read part of his blog post on this and had already felt convicted by it. This reminded me that I really need to do something about this. By the time Dan was done showing the Little Big League clip about the house painting problem (the one where the team is trying to help the young star with his math homework problem) and Dan closes by stating that this clip is emblematic of what concerns Dan about math teaching, it has really hit home to me that I have been that math teacher that concerns him about math teaching. I have done all these things, and even worse, I have tended to skip the application problems in favor of getting through the material. But I also know that this doesn't work and I need to change. That's why I am here in Orlando. My sincere hope is that I learn how to make the changes I need to and improve my math teaching.
The next section of Dan's talk is about how to set up the application problem. He takes a typical problem and breaks it down. In most textbooks, you have an image (maybe some clip art), the setup of the situation, the given information, some steps (textbooks tend to either do the process for the student in the steps or make the problem more difficult), and finally the task. Dan breaks this down into 4 steps:
Visualize the problem (here's where the multimedia we are familar with comes in)
Abstract the problem (what information do we need to solve the problem - textbooks give them this)
Decompose the problem (textbooks do this for students all the time - these are the individual parts of the problem)
Verbalize the problem (this is almost always the last thing in a textbook and it should be the first thing)
My notes as Dan talked through this process:
Verbalizing the problem is the very end of the problem in a textbook but in our head at the very beginning.
In textbooks, problems are decomposed to the point that are bite-sized and each point is trivial.
If I suggest the formula to the students in the problem, both teacher and student lose. Let students decompose the problem.
Separate the tasks, just like they are in life.
We have made math boring and challenging in all the wrong ways. Math is boring when we just give the students the formula, they know how to use it and they have the answer. It is challenging in the wrong ways when students have no idea where to start because they don't know the formula.
Dan then walks through taking a textbook problem and revamping it. He takes a fairly typical perimeter problem (it involves building a fence with boards that are spaced 1/4 inch apart and it has a very typical drawn picture - you all know what I am talking about) and then proceeds to revamp it. He starts by finding a better visual using Google Maps. Then he draws in the fence and asks for any questions. You all know what the question is - the picture draws it out. Then he asks what do you need to solve the problem? He fills in that information and then you have at it.
Dan has blogged before about the whole idea of three acts to a problem. I previously got the 1st act and mostly got the 3rd act, but really struggled with the 2nd act. I guess I didn't really understand what all we provide in that part. I knew that the 2nd act was where the problem was solved, but I guess I wasn't totally clear on how much (or how little) information we provide to students. Watching Dan today transform ye old boring textbook problem into something more interesting helped make the whole thing click for me. It also made me feel that this was something I could do. I have read bits and pieces of his blog before and to be honest, it is a bit intimidating to see all this great and wonderful math that he is pulling together with multimedia and real world context. I tried to play around with the whole WCYDWT idea (see Wii Bowling) and didn't get anywhere I thought I would with it. The whole experience left me somewhat frustrated and still intimidated. Then I did a foray into #anyqs with the comparison of different maps for our Houston trip (which if I were to do again in my class I would revamp more towards what Dan did at the beginning with his parents' trip) and felt like I had a better grasp on how to do the 1st act of the problem. When I read his post on the three acts of the problem after I had done the Houston #anyqs thing, I was back to being confused. At the moment, I am at a point where I feel I can at least attempt this whole idea of finding something real-world and setting up a problem based on something I have seen in a text book. I am still not sure I am ready to come up with something totally on my own.
I do have to say that since Dan posed the original #anyqs challenge, I am finding more and more math around me. It pokes in my head when I least expect it (and sometimes that's a real curse, gosh darn it!). However, I have not gotten to the point where I can find that stuff and it's something accessible to my students. Maybe I just don't give them enough credit. I've never taught like this. I have said many times, I am very much a traditional teacher. Putting something in front of my students and looking for questions and having them solve it (and be successful) is not something I've done before. This year will be the first time I have done that to completion ever (and I have just finished my 19th year of teaching). Probably the biggest thing that scares me is that I don't feel like I know how to use these types of problems. Do I put them in front of my students before they have had instruction on the mathematics they need to solve the problem and let them have at it? If I do that, will they say to me at some point, "Mrs. Henry, we don't know how to do this. Can you teach us?" Do I let them come up with their own methods to do that, Common Core Curriculum be damned? (I think that's what I'm "supposed" to do - not just teach them whatever the skill is.) Where does the instruction part come in? And so the questions go on in my head...
Dan also did go through the pyramid of pennies problem that @dandersod originally brought to the #anyqs thread on Twitter in May or June. It was also really cool to see this problem discussed in the same manner. It was also good to see how Dan would present the information and the answer.
Although Dan never used the whole idea of "three acts" by name, his presentation (to me) went through the three acts. I did find it easier to grasp. At the end, he talks about verifying the answer and whether students "buy" the answer. The analogy he uses is if he's selling you a knife and he tells you that it cuts through anything. You say, I have an old shoe, show me. He says, it says in the pamphlet it cuts through anything. But you want to see it. He keeps says that the pamphlet says it does, so that's good enough. We do the same thing when we give kids the answer (or have them look in the back of the book). It's better to show them the answer.
All in all, an excellent presentation by Dan. I left it feeling that this is something I could do, which I haven't felt before and that I have a minimum starting point (my textbook). I also know I have other places I can look (internet, news, and of course, the world around me) - I just have to get better at it. Most of all, I have to not give up on it. That is going to be the hardest part. Thanks Dan, for an excellent presentation. Well done.
Rather than sum up everything he talked about, I will hit some of the high points. Some what he presented are parts of blog posts he has done this summer.
Dan opened with the story of his favorite horse, Clever Hans. If you are not familiar, Clever Hans is the horse around the turn of the century who could predict the answer of any mathematical question. When researchers tried to figure out what was so special about Clever Hans, they figured out that if the person who questioned him didn't know the answer or wasn't visible to Clever Hans, he would miss the question. Basically, what Dan is getting at here is something most of us do as teachers is like what Clever Hans' questioners did - we give away whether a student is correct by any one of a number of visual or verbal cues. Ultimately, we are creating a bunch of Clever Hans' - students who can figure out if they're right, instead of Smart Hans', who can reason and make sense of what they are doing mathematically and find the correct answer on their own.
When Dan talked about the Clever Hans story and got to his point, I felt very convicted. I do this too. I need to get away from that and work on being less helpful. In a later discussion at my strand session (I'm in Intermediate Algebra), I was sitting at a table with Hank Kepner (past NCTM president). He was talking about a similar thing in his classroom when he taught. I asked him, what do you do when the student presents you with a correct solution. His response was to ask them why it was correct. He wants his students to be able to defend their answer and know why the answer is good - the process is more important than the answer. Between these two things, I realize that I really need to learn about questioning and how to be more effective in the classroom. Less Clever Hans trainer and more a guide. Need to figure that out, and soon.
Enough chasing rabbits for now and back to Dan. He then went through a bit about curriculum and talked about application problems - problems that are practical (when am I ever going to use this?) and/or explanatory (even though we aren't using math, math is using us). For practical, he uses the example of helping his parents figure out whether it was cheaper to drive and park at the SF airport or drive part-way to (I forget where), park and take the shuttle. For explanatory, he uses the basketball problem.
Another point Dan made was our textbooks are set up to connect problems to previously worked examples – our textbooks even tell us where to find the examples. Too fill-in-the-blanky. Don’t reduce math to filling in blanks and working fixed examples. This is something else I am guilty of. Give the example and problems are similar to them. I had already read part of his blog post on this and had already felt convicted by it. This reminded me that I really need to do something about this. By the time Dan was done showing the Little Big League clip about the house painting problem (the one where the team is trying to help the young star with his math homework problem) and Dan closes by stating that this clip is emblematic of what concerns Dan about math teaching, it has really hit home to me that I have been that math teacher that concerns him about math teaching. I have done all these things, and even worse, I have tended to skip the application problems in favor of getting through the material. But I also know that this doesn't work and I need to change. That's why I am here in Orlando. My sincere hope is that I learn how to make the changes I need to and improve my math teaching.
The next section of Dan's talk is about how to set up the application problem. He takes a typical problem and breaks it down. In most textbooks, you have an image (maybe some clip art), the setup of the situation, the given information, some steps (textbooks tend to either do the process for the student in the steps or make the problem more difficult), and finally the task. Dan breaks this down into 4 steps:
Visualize the problem (here's where the multimedia we are familar with comes in)
Abstract the problem (what information do we need to solve the problem - textbooks give them this)
Decompose the problem (textbooks do this for students all the time - these are the individual parts of the problem)
Verbalize the problem (this is almost always the last thing in a textbook and it should be the first thing)
My notes as Dan talked through this process:
Verbalizing the problem is the very end of the problem in a textbook but in our head at the very beginning.
In textbooks, problems are decomposed to the point that are bite-sized and each point is trivial.
If I suggest the formula to the students in the problem, both teacher and student lose. Let students decompose the problem.
Separate the tasks, just like they are in life.
We have made math boring and challenging in all the wrong ways. Math is boring when we just give the students the formula, they know how to use it and they have the answer. It is challenging in the wrong ways when students have no idea where to start because they don't know the formula.
Dan then walks through taking a textbook problem and revamping it. He takes a fairly typical perimeter problem (it involves building a fence with boards that are spaced 1/4 inch apart and it has a very typical drawn picture - you all know what I am talking about) and then proceeds to revamp it. He starts by finding a better visual using Google Maps. Then he draws in the fence and asks for any questions. You all know what the question is - the picture draws it out. Then he asks what do you need to solve the problem? He fills in that information and then you have at it.
Dan has blogged before about the whole idea of three acts to a problem. I previously got the 1st act and mostly got the 3rd act, but really struggled with the 2nd act. I guess I didn't really understand what all we provide in that part. I knew that the 2nd act was where the problem was solved, but I guess I wasn't totally clear on how much (or how little) information we provide to students. Watching Dan today transform ye old boring textbook problem into something more interesting helped make the whole thing click for me. It also made me feel that this was something I could do. I have read bits and pieces of his blog before and to be honest, it is a bit intimidating to see all this great and wonderful math that he is pulling together with multimedia and real world context. I tried to play around with the whole WCYDWT idea (see Wii Bowling) and didn't get anywhere I thought I would with it. The whole experience left me somewhat frustrated and still intimidated. Then I did a foray into #anyqs with the comparison of different maps for our Houston trip (which if I were to do again in my class I would revamp more towards what Dan did at the beginning with his parents' trip) and felt like I had a better grasp on how to do the 1st act of the problem. When I read his post on the three acts of the problem after I had done the Houston #anyqs thing, I was back to being confused. At the moment, I am at a point where I feel I can at least attempt this whole idea of finding something real-world and setting up a problem based on something I have seen in a text book. I am still not sure I am ready to come up with something totally on my own.
I do have to say that since Dan posed the original #anyqs challenge, I am finding more and more math around me. It pokes in my head when I least expect it (and sometimes that's a real curse, gosh darn it!). However, I have not gotten to the point where I can find that stuff and it's something accessible to my students. Maybe I just don't give them enough credit. I've never taught like this. I have said many times, I am very much a traditional teacher. Putting something in front of my students and looking for questions and having them solve it (and be successful) is not something I've done before. This year will be the first time I have done that to completion ever (and I have just finished my 19th year of teaching). Probably the biggest thing that scares me is that I don't feel like I know how to use these types of problems. Do I put them in front of my students before they have had instruction on the mathematics they need to solve the problem and let them have at it? If I do that, will they say to me at some point, "Mrs. Henry, we don't know how to do this. Can you teach us?" Do I let them come up with their own methods to do that, Common Core Curriculum be damned? (I think that's what I'm "supposed" to do - not just teach them whatever the skill is.) Where does the instruction part come in? And so the questions go on in my head...
Dan also did go through the pyramid of pennies problem that @dandersod originally brought to the #anyqs thread on Twitter in May or June. It was also really cool to see this problem discussed in the same manner. It was also good to see how Dan would present the information and the answer.
Although Dan never used the whole idea of "three acts" by name, his presentation (to me) went through the three acts. I did find it easier to grasp. At the end, he talks about verifying the answer and whether students "buy" the answer. The analogy he uses is if he's selling you a knife and he tells you that it cuts through anything. You say, I have an old shoe, show me. He says, it says in the pamphlet it cuts through anything. But you want to see it. He keeps says that the pamphlet says it does, so that's good enough. We do the same thing when we give kids the answer (or have them look in the back of the book). It's better to show them the answer.
All in all, an excellent presentation by Dan. I left it feeling that this is something I could do, which I haven't felt before and that I have a minimum starting point (my textbook). I also know I have other places I can look (internet, news, and of course, the world around me) - I just have to get better at it. Most of all, I have to not give up on it. That is going to be the hardest part. Thanks Dan, for an excellent presentation. Well done.
Monday, July 25, 2011
Understanding by Design Chapter 9 - #sbarbook Mon 7/25/11
jsb16 OK. Who wants to start #sbarbook? What did you think of chapter 9?
gwaddellnvhs Who is here for #sbarbook tonight? @jsb16 and are hosting.
jrykse present. #sbarbook
gwaddellnvhs #sbarbook Chap 9 was where the rubber really hit the road for me. Very detailed and focused on planning. It is what actually matters.
gwaddellnvhs #sbarbook the "whereto" makes a lot of sense in the planning process. Spend more time planning, and in class the learners do the work.
jsb16 Trying to integrate modeling, #anyqs, #wcydwt, and WHERETO & my brain is overflowing #sbarbook
gwaddellnvhs @jsb16 #sbarbook but really, #anyqs and #wcydwt speak to the "hook" the "where" and the "reflect & revise". They can be very simpatico!
jrykse I think the whereto will help clean up lessons. I have some missing pieces. #sbarbook
jsb16 @gwaddellnvhs Didn't say they wouldn't work well together. Just different from how I learned #sbarbook
gwaddellnvhs @jsb16 #sbarbook I agree. The way I was taught to develop a lesson plan was very bad. Very teacher focused, not learner or results focused.
jsb16 #sbarbook Really liked the "We take a different view." (pg 202) Brings in some of the passion/interest-based angle.
gwaddellnvhs #sbarbook Page 192, "What is the best use of time spent in & out of classroom." Reminded me of "Rethinking Hmwk" by Vatterott. It all fits!
jsb16 #sbarbook Also different from how my HS teachers planned & different from how PD is run. Not sure how it should feel. @gwaddellnvhs
gwaddellnvhs @jsb16 #sbarbook We are forcing our PD to run along side UbD. It can't be optional to teach well. It has to be an expectation (in my dept.)
jsb16 #sbarbook There's a bit about teaching transfer explicitly. How do you do that in your classes?
gwaddellnvhs @jsb16 #sbarbook - "teaching transfer" badly.
gwaddellnvhs @jsb16 #sbarbook sorry about the snark. That is a struggle. we did not spend much time working on that last year, and it showed.
gwaddellnvhs @jsb16 #sbarbook it is something this year we are going to work hard on attempting (not sure if we will succeed, but we will try.)
jrykse @gwaddellnvhs We seem to spin our wheels tackling tasks instead of being able to talk about student learning & getting better. #sbarbook
gwaddellnvhs @jrykse #sbarbook there is some contention. 2 teachers who refuse to participate. I think this year it will be the "good" plc and the rest.
gwaddellnvhs @jrykse #sbarbook we do have an agenda that explicitly works against the "task" focus. It helps to have the agenda set, and
gwaddellnvhs @jrykse #sbarbook and strong personalities that keep it from being hijacked by the "get it done and go home" persons. It takes more time tho
jsb16 @gwaddellnvhs #sbarbook @jrykse I think I'm the only one in my department investigating modeling and #sbar.
jrykse Catching up on #sbarbook tweets, had a washer emergency, turns out I don't have to buy new one, circuit was tripped. Phew.
gwaddellnvhs #sbarbook any other comments on the "whereto"? @jrykse @jsb16
gwaddellnvhs @jsb16 @jrykse #sbarbook It is hard when you are alone. Thank goodness for social networking! and success breeds success. it will pay off.
jsb16 #sbarbook I think it'll be useful, eventually. I'm not sure I have the assessment part clear enough in my mind to work on this yet. :(
jrykse @gwaddellnvhs @jsb16 The catcher in the rye example on p199 spoke to me. Now to do that in math. #sbarbook
jsb16 @jrykse #sbarbook I liked that example, too. Trying to translate it into physics...
gwaddellnvhs @jsb16 @jrykse #sbarbook my initial idea: Handicapped ramp at school is not built to spec. We must learn all necessary math to show it is.
gwaddellnvhs @jsb16 @jrykse #sbarbook This is for a linear function review, and I would set out all pieces and at the end go out side and they measure
jsb16 @gwaddellnvhs #sbarbook My idea: elementary school across busy street from park: can kids cross safely?
jsb16 #sbarbook That's for constant velocity motion, possibly extending to constant acceleration motion.
jrykse @jsb16 Then students make a case to department of transportation whether one of those overhead crosswalks should be built. #sbarbook
jsb16 @jrykse #sbarbook Exactly. I was thinking that the audience for the project would be the city planning department.
gwaddellnvhs @jsb16 @jrykse That is really good! I like that idea. #sbarbook It is good the audience is someone besides us, the teacher.
jsb16 @gwaddellnvhs #sbarbook Thanks. I need to work on rubrics and checklists and so on, to help myself (and students) get it together.
jsb16 #sbarbook And I need video of the street and pictures of the school & park and measurements to allow students to collect data...
gwaddellnvhs @jsb16 #sbarbook That is one difficulty with this method. More work up front for us. But the payoff of the learners working more is worth it
jrykse @jsb16 @gwaddellnvhs Rubrics, that another thing I learned from #sbarbook I do badly.
jsb16 #sbarbook I hope to make time to post the project on http://physicsadventures.blogspot.com/ and maybe work out some of the kinks that way.
druinok I can't wait to read tonight's #sbarbook discussion - looks really good so far!
jsb16 #sbarbook Next Monday for chapter 10?
jrykse @jsb16 I can do Monday. #sbarbook
gwaddellnvhs @jsb16 #sbarbook, next monday sounds great to me.
jsb16 @gwaddellnvhs @druinok #sbarbook Monday, 9:30 for Chapter 10?
gwaddellnvhs @jsb16 @druinok agreed. Monday, 9:30 for Chapter 10. #sbarbook
jsb16 #sbarbook OK, next Monday it is for Chapter 10.
Tuesday, July 19, 2011
Understanding by Design Chapter 8 - #sbarbook Monday 7/18/11
jsb16 NP: #sbarbook Ch7: in which I flounder trying to get a handle on designing assessments to get at student understanding of velocity.
jsb16 NP: #sbarbook Ch7: http://t.co/SWlJUtB in which I try to get a handle on designing assessments to get at student understanding of velocity.
druinok Okay ladies and gents, who all is here for Ch 8 of #sbarbook?
gwaddellnvhs @druinok #sbarbook Woohoo I am here, and twitter is working again for me suddenly!
jsb16 I'm sort of here #sbarbook. Haven't finished the chapter, though.
fourkatie Here for #sbarbook, but Twitter says I'm following 0 people so not seeing much!
druinok Okay, so any first thoughts on Ch 8? Do any of you use rubrics now when grading? #sbarbook
gwaddellnvhs @druinok #sbarbook I have some bad ones I created that I used. After this chap I know why teachers before me used rubistar. consistency.
druinok I liked the idea that an explicit goal implies the criteria needed for the rubric, even before the task is designed (pg176) #sbarbook
druinok For me, the issue with rubrics is that it takes so long to get it perfected :( I did like their guide on how to set one up tho #sbarbook
gwaddellnvhs @druinok #sbarbook and just because you give feedback with a rubric doesnt mean it has to be a grade. grade could come later after revision
jsb16 @druinok #sbarbook I use rubrics, but I've never happy with them. Not fond of Rubistar. I like @DataDiva's rubrics.
druinok @gwaddellnvhs I know w/ the AP rubrics, they start w/ a draft and use hundreds of student papers to revise #sbarbook
eduz8 MT I totally agree. Change them every time. @druinok For me, the issue with rubrics is that it takes so long to get perfect #sbarbook
jrykse Anyone able to get back on for #sbarbook?
druinok @gwaddellnvhs but obviously in our classrooms, we don't have unlimited resources with which to perfect the descriptors #sbarbook
druinok @jsb16 I've not seen her rubrics - do you have a link? #sbarbook
gwaddellnvhs @druinok #sbarbook that is the problem isn't it. Bouncing off of the @datadiva comment. WOW!!! I have not seen her site before. Nice.
jsb16 @druinok Hang on while I find them back... #sbarbook
druinok I also really liked the self-assessment piece (2 ?s) on pg 184... #sbarbook
jsb16 #sbarbook Here's @DataDiva's 'Quality Rubrics' wiki: http://qualityrubrics.pbworks.com/w/page/992395/Home
gwaddellnvhs @druinok @jsb16 #sbarbook I wonder how many times I have given invalid assessments and though later, why didn't they get it?
jsb16 I like the 6facet rubric (pg 178-8) #sbarbook. I'm thinking that the top level is beyond A+ for HS, though.
druinok @gwaddellnvhs exactly! I think that's the hardest part :( and the same issue w/ self-assessment of the rubric #sbarbook
gwaddellnvhs @jsb16 #sbarbook Should it be though? if many (not all) assignments are built around they honeycomb, they should be able to reach up to it.
druinok @gwaddellnvhs sometimes when I've used rubrics, I get frustrated b/c their overall score doesn't seem to match the output :( #sbarbook
justbugnu @druinok I really liked the self-assess on that page as well. #sbarbook
gwaddellnvhs @druinok #sbarbook both ways on score not matching.I had terrific work earn low score. Was rubrics expectations not met, or work truly bad?
jsb16 @gwaddellnvhs #sbarbook In physics? Thorough, inventive, powerful, illuminating... Grad students still aspire to the kind of understanding.
druinok @gwaddellnvhs or poor descriptors on rubric? good question #sbarbook
justbugnu #sbarbook I really liked the self-test for assessment ideas on pg 187. I'm going to use that as I plan.
gwaddellnvhs @jsb16 #sbarbook harder in physics, you are right. (my degree is in physics, I understand!) But pushing them can't hurt (I hope).
druinok I think I need to take their advice on starting small w/ rubrics, just understanding and performance at first #sbarbook
jsb16 @gwaddellnvhs #sbarbook I'm thinking that 2nd-from-top will be A+, & top will be "extra credit".
druinok @jsb16 @gwaddellnvhs you are referring to the rubric on pg 178? #sbarbook
eduz8 #sbarbook Rubrics are tough. Trying to predict paths and quantify feedback seem to limit options and make a task less "authentic".
gwaddellnvhs @druinok @jsb16 #sbarbook yes. That is a tough rubric on 178.
druinok @jsb16 @gwaddellnvhs I agree that top line is pretty intense for most kids #sbarbook
jsb16 @druinok @gwaddellnvhs #sbarbook Yes. The top level seems a discouragingly high bar for students unused to SBAR.
gwaddellnvhs @jsb16 @druinok #sbarbook I think it takes a lot of scaffolding to begin at a lower level, and by the end of the year work up to this (178)
druinok @eduz8 agreed, I like the "make piles and jot why on sticky-notes" approach they had, but crazy amounts of time #sbarbook
jsb16 #sbarbook Really wish I could run through the refining process on p181 with actual student work & colleagues.
druinok @jsb16 I don't know that I would have a large enough sample size to refine well :( #sbarbook
gwaddellnvhs @jsb16 #sbarbook I have several teachers that collaborate with me on this type of thing in my department. That way we help each other.
gwaddellnvhs @jsb16 #sbarbook I strongly recommend it! When several people are coming up with good material based on this, it make light of the work.
eduz8 @druinok I find that the refining is mostly in my head: my goals, my purpose. Rather than student work. #sbarbook
jsb16 @druinok #sbarbook I don't think it's a matter of sample size. Even a small class can have variety of understandings.
druinok @eduz8 I think part of my struggle is so many rubrics are very subjective and that's tough :( #sbarbook
druinok @jsb16 For the purposes of refining the rubric though - if you are using student samples to refine the descriptors #sbarbook
jsb16 @gwaddellnvhs #sbarbook I'd love to, believe me. A matter of convincing colleagues that I'm not trying 2 get them 2 do my work or vice versa
gwaddellnvhs @jsb16 #sbarbook I guess that is where twitter comes in then, huh! We need to find you some like minded physics teachers.
jsb16 @druinok #sbarbook It's still not a sample size issue. You're looking for examples of work at each level. Iterative, rather than statistical
jsb16 @gwaddellnvhs #sbarbook Also a matter of getting permission/forgiveness for posting student work on the interwebs... :)
druinok @eduz8 I struggle writing the descriptors in a clear enough manner to easily differentiate between the levels #sbarbook
gwaddellnvhs @jsb16 #sbarbook If you use post-its to cover identifying part, take pictures or scan w/o names, should be no problem. Just don't post it.
jsb16 @druinok @eduz8 #sbarbook Think fewer levels would be easier to write?
gwaddellnvhs @druinok @eduz8 #sbarbook I think practice with writing the descriptors is key here. The more we practice, the easier it will be.
druinok @gwaddellnvhs @eduz8 @jsb16 To be perfectly honest, dont know how much of this I will implement this year - it's very overwhelming #sbarbook
eduz8 #sbarbook Ever have students use your rubric to provide feedback on peers?
jsb16 When I blog this chapter #sbarbook (probably tomorrow), I'll post some of the rubrics I used this year. Hoping people will comment.
gwaddellnvhs @druinok @eduz8 @jsb16 #sbarbook like with anything worthwhile, baby steps!
jsb16 @eduz8 #sbarbook I write a separate rubric for peer assessments, focused more on process than understanding.
eduz8 #sbarbook I am finding thinking about bid ideas to bind my course together helpful. Different. Build from there. http://bit.ly/qyWqIl
eduz8 @jsb16 How are they different? #sbarbook
druinok @gwaddellnvhs Just be happy I've continued reading - I was about to chuck this book a few chapters back :) #sbarbook
gwaddellnvhs @druinok #sbarbook Nooo! Honestly, I think this is the most useful, and difficult, book I have read since becoming a teacher.
jsb16 @eduz8 #sbarbook 4 a lab report, process is: are graphs clear? Questions answered? Conclusion stated? Understanding is: r conclusions valid?
eduz8 @jsb16 #sbarbook Why do you not have students provide feedback on the validity of conclusions?
jsb16 @eduz8 #sbarbook Their grasp of validity tends to be right v. wrong and often accompanied by insults &/or sucking up. Trying to avoid emo...
druinok Okay #sbarbook folks, the convo seems to be winding down - what do you want to do for Ch 9? What day is best for you?
jsb16 @druinok #sbarbook Next week! I need time to process and start experimenting with all these ideas...
fourkatie Sorry I missed #sbarbook. I still have 0 follows/followers, but I'm seeing some posts in my stream now.
jreulbach @fourkatie Sorry I missed. Fam reunion this week. It's going to be hard to get to anything this week. #sbarbook
druinok Also guys, once August gets here, I don't know how reliable I will be w/ #sbarbook just fair warning :)
druinok any other feedback on when to do ch 9 of #sbarbook? (If it's next week, I will need a volunteer to lead it) (also, ch 9 is long)
gwaddellnvhs @jsb16 @druinok #sbarbook I agree, next monday.
gwaddellnvhs @druinok #sbarbook I can help lead it if it is Monday.
jsb16 @gwaddellnvhs @druinok #sbarbook Likewise: I can help out if it's next Monday.
druinok Okay then, next Monday night it is :) #sbarbook
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