Saturday, April 30, 2011

WCYDWT - Wii Bowling Day One

My Math 1 students finished their test with a lot of time to spare, so I put up the Wii Bowling pictures I had taken (see this post) and had them take out a piece of paper. I asked them to write down what they noticed and wondered about what they saw in the pictures (similar to what @maxmathforum suggested in this post). My thought with starting with it today was to get an idea where they were at and try to come up with a game plan for Monday. Here are the responses I got (and not everyone responded):

Class One:
  • Why is Mommy still pro when Grace has higher points than Mommy?
  • Why can't we play bowling in math?
  • Why is there only one pro?
  • The numbers change
  • Only 1 is pro
  • highest number is 1005
  • lowest is 65
  • different scores on both games
  • Why is there an arrow point down by your name then on the second its pointing up"
  • What are the negative and positive numbers beside the names?
  • I wonder how bad I'd beat you in Wii bowling.
  • I'm wondering how you got a pictre of that on your computer.
  • A couple of students wrote what was on the slides (number-wise)

Class Two:
  • The first game you lost but your skills points was the most but you won the second game but had the same amount of points.
  • Cade's skill in the first game went up. Second game it went down.
  • Mom dropped from pro by 62, then she went up by 8 and made it back.
  • Why do you have a higher skill level than your kids?
  • How old are each of the people?
  • Who's best?
  • The arrow on the first screen is going up on "Mommy."
  • Your daughter wont he first round.
  • You went down 62 points.
  • You weren't pro the first game, then you were the second?
  • It says you are 1,000 pro but your score is 997.
  • You have more points but you did not win.
  • Did you play again?
  • What are your averages?
  • How many open frames did you have? (Note - I layered the pictures so they could not see the individual frames.)
  • What happened with the skill level?          \
  • What is this about?                                      These three questions are all by the same student.
  • How many points did you go up? Down?  /
  • What do you usually bowl?
  • How many points did you go up from the first game?
  • What does Grace usually bowl?
  • Does Cade practice?
  • Why did you get better also you played?
  • Is it about math?
  • How did you level up to a pro?                   \
  • Was it easy to level up?                                \
  • Was it fun beating your kids?                         \
  • How good of a bowler are you in real life?     / These statements are all from the same student.
  • I noticed you leveled up to a pro!                  /
  • You lost to your kids?                                  /
  • I play Wii and I know what all of it means.
  • Why are you red?
  • Who's Grace?
  • Who's better at the game?
  • In this class I had a couple of students who wrote question marks or that they were confused.
 I feel like this went nowhere. There were a couple of students in the second class who asked some questions that we might be able to take somewhere. Most of my students in my first class have no clue and/or didn't follow directions (I only had papers from about half). The whole process of getting them to write questions was incredibly slow and painful - I had no idea what else to ask them or say to get them to come up with (math-related) questions and I didn't want to put any ideas in their head of what they were supposed to be asking. I look at this list and I feel like I didn't do something "right" or somewhere I missed the boat. This really reinforced for me that I need to read what others have done with WCYDWT this weekend as I reflect and regroup.

Here's the real problem for me at this point - I have no clue where to take this from here. My original thought was to have them bowl as "guests" on my Wii to get some scores from scratch but we'd have to be able to complete bowling during the (50 minute) class period to get data for them to work with. I had thought about dividing them into teams and having each person on the team bowl a frame so that everyone would have a chance to play. I'm not sure how many games we'd get through, but I could take my camera and take similar pictures as I did at home. Then the following day in class we could (hopefully) do something with the data. But again, I have no clue what do after this. I was hopeful to have some more mathematical questions.

It's late, but I wanted to get the thoughts out while they were still somewhat current in my mind. I'll continue to add to this as I have more time to ponder. I am certainly open to any suggestions and comments.

Monday, April 25, 2011

How to incorporate WCYDWT (Rich Problems) into math class?

So, I have no idea how to bring in WCYDWT and/or Rich Problems into my math classes. I really was never taught in college how to do something like this. So I have been tweeting, asking how to start. Here are some responses I got today.

@maxmathforum @ putting up a problem scenario (video, text,...) and asking students What do you Notice? What do you Wonder? in a think-pair-share
Me (@lmhenry9) @ What if you are working with students who are unaccustomed to "wondering" about things mathematically?
@maxmathforum @ on the one hand, that slows things down. On the other, I've never had a class without a wonderer or two. In LOTS of diff. schools.
@ I love problems that generate controversy, a yes/no answer, a chance for kids to "wager" on an answer. That's a way to wonder...
Me @ Do the other students then start to join in? I'm working with lower level students who aren't real thrilled about math.
@ This is something completely new to me - do I just put out the scenario and hope they wonder abt it? Just see where it goes?
@maxmathforum @ some kids spend all yr wondering "why is the paper red?" but most start to generate questions and some start conjecturing well
@ the expectation that they write 5 noticings and wonderings on their paper, share with a buddy, and then share out seems to work.
Me @ This is the situation I want to bring to them - and I'm trying to figure out how to go with it.
@maxmathforum @ calling early on kids who rarely contribute means they say obvious/important noticings and as you solve, you refer back to theirs
Me @ That makes sense. Hadn't quite thought of it that way. That would also engage them (hopefully).
@maxmathforum @ it builds their confidence and buy-in when you say, "remember that important thing Tasha noticed..."

Me @ Part of what I am struggling with (esp since I'm very much a traditional teacher) is how the content fits in.
@ Does the problem introduce the content or have students had the content previously?
@maxmathforum @ since it's a real context, the kids' wondering might really flow. Like, "how can I get to this skill level?" or "why'd his go up?"
@ I believe that you don't learn without a question in your head. Like, "how does my score go up?" and then the content follows.
@ I'm agnostic about delivering the content after the ? is generated. If the ? is well understood, the kids will hear and make sense
Me @ When I first looked at it, I wondered whether there was an equation to determine how your score went up.
@maxmathforum So they may wonder about it & try to figure it out with what math they know. If they don't have enough math knowledge, then intro new content?

@maxmathforum @ that's what I'd do
Me @ Thanks so much for your help - I greatly appreciate it.
@maxmathforum @ happy to get to think about helping kids become problem-solvers! I'll comment on your blog too if I think of anything else
@dandersod @ you can start off pretty small with the wcydwt stuff. how many jelly beans in a jar? that brings up volume.
@ getting the students to "buy in" is important. you can do this by writing down their guesses. everyone likes to try and be right.
Me @ I primarily teach algebra - what would you suggest is a "small start?"
@dandersod @ Picture of you next to a tree/building. How tall is the tree/building? Proportions and ratios?
@maxmathforum @ cell phones... i brought in my bill and had kids figure out how much my overtime mins cost. They decided I needed a cheaper plan.
@dandersod @ maybe a doubling idea?
Me @ Am I correct in my assumption that wcydwt cannot be used with everything we are to cover in the HS math curriculum?
@ How often do you use wcydwt in your classes?
@dandersod @ 2-3 times a month maybe? it's tough work to get setup.
Me @ That's good to know. I wasn't sure whether people who did wcydwt/rich probs. did them all the time or just every so often.
@KaminskiTerry @ definitely cannot use WCYDWT with everything in curriculum. @ Only uses it about once every week or two
Me RT @ and on non wcydwt days, what does class look like? @ @ What is the answer?

@KaminskiTerry @ @ On non wcydwt days the class may look very similar to what it does right now.
@druinok @ @ can you expand on that? Do you mean traditional?
Me @ @ @ So what about those who say we should be doing prob solving daily (and w/ rich problems)?

@KaminskiTerry @ @ @ Sometimes we need to teach the kids the skills. However, we can still have them thinking.
@ @ @ Give the students the answer and have them create thequestion.
@druinok @ and how long of a process is it to get there?
@dandersod @ @ @ selfishly, it makes the classroom much more interesting for me. Kids get into it too.
@KaminskiTerry @ @ @ I agree. U have to try it and refine as u go
I should also add that @mrautomatic tweeted that I should check out Dan Meyer's blog and that's already on my "to do" list.
So... I have some answers from a couple of people.  What about others? How do you start with WCYDWT and/or rich problems in your classroom? How does it work? Do you do it every day? If not, how do the rest of the days go in your classroom? At NCTM, several people ("experts" if you will) expressed that we should be doing rich problems in our classrooms daily. Do we try to accomplish this iin our classrooms?. How do we get closer to that ideal?
Please take a few moments and respond to any and all of these questions in the comments. I'd love to see some good discussion about it - there are other teachers who have the same questions and they would benefit also. Thanks!

Saturday, April 16, 2011

My first foray into WCYDWT

Well, be gentle with me, dear readers - this is a total new venture for me. I have been bouncing this in my head for a while but I have no idea where to take this. My target audience is freshmen who has some Algebra experience have low math skills (my Math 1 class). I am hoping to do something with this in the next few weeks. I feel I have nothing to lose - and possibly lots to gain.

When I have played Wii Bowling with my kids, it keeps track of our scores.

After we are done, it gives us a "skill level." I suspect it's linear but I want to know how it comes up with it.

So here are the thoughts I have had about this:
1) I want the kids to Wii Bowl in class. I think that's my buy in with the kids. My classes are mostly boys but this Wii game is accessable to all. You can bowl as a guest and see scores.

2) I have no clue how to develop this activity. I have no idea where to start or where to have the kids start. I know I need to take some time to head over to dy/dan and look at the other WCYDWT so I can get a better idea. As I said at the beginning, I have a little time until I would do this, but not much. Hence, I need some help and feedback from you all as to where to go with it.

3) I purposely skipped writing linear equations with this group because I didn't feel they could do it. I am now thinking maybe if I frame it in this context that maybe they will surprise me. So I know going in they don't have any background on writing linear equations. But, they have done slope and writing equations if they are given the slope and the y-intercept, so they may be able to get there.

Please help! Any and all suggestions are greatly appreciated.

NCTM11 - Achievement and the Common Core

The last NCTM session I attended was Matt Larson's "Supporting Students' Achievement of the 'Common Core.'" I had initially marked this one, then after 3 CCSS sessions yesterday, debated whether to go and ended up here after the other session I had looked at was stuff I already knew. This was the best of the 4 Common Core sessions I attended because I felt he gave us things we could look at on a district level. The other three sessions I attended gave suggestions but they were things that were out of my and my district's control.

Larson spoke quickly, but he did give us his email at the end of the session to get his powerpoint. I have uploaded it to my here. Once again, these are my notes from the session and they are somewhat scattered because of the amount of material and the speed he spoke.

Research tells us about a challenging curriculum that the keys are A^2 - Alignment and Access.

Most states report a high rate of student proficiency on their state tests, but if you look at the National Assessment of Educational Process (NAEP), it's not good. All states except Massachusetts are reporting high percentages of students (like 70, 80, 90%) as being "proficient" in math but the NAEP shows a much lower percentage of students who are proficient. The reason the NAEP is significant is it is an international benchmarked test.

Students do well on what they have the opportunity to learn. Many of our students don't have the opportunities to learn material (see later on).

Next year's kindergarten students will be the first ones to take the new 3rd grade assessments.

There are only 3 people who really wrote the CCSS. I thought that was rather interesting. As earlier presenters have said, mathematical understanding and procedural skill are equally important.

In most location we give students different opportunities to learn math - we have a high, medium and low track or grouping of students. It is important that all student have access to the same curriculum. Larson suggested we get rid of low track at the high school level and have all freshmen students take Algebra 1. The research he cited says that they will do better than we expect. We cannot continue to do what we are doing - have all students take Algebra 1 but have a low track and a regular track. This solution limits students in what they can learn content wise and it ultimately limits what they can do once they leave high school. A better solution is to have a double period Algebra 1 class for students who are struggling and to use varied strategies with them to help with their mathematical understanding.

We track our teachers also. Our "best" teachers get the high end courses - Calculus, Pre-Calculus, etc. Our newer and/or "less effective" teachers get the Algebra 1 and the lower end kids. We need to evaluate who gets assigned  what to teach. Right now, students who struggle end up with the least effective and experienced teachers. These students should be exposed to the best teachers, however the best teachers shouldn't have 6 periods of this either.

Larson reminded us of the "teacher as the guide on the side, not the sage on the stage" philosophy. His research has shown that the teachers' choice of strategies to use in the classroom affects how the students achieve. Teaching has 6-10 times as much impact on achievement as all other factors combined. (my emphasis) For as much as we get bashed as teachers - we have to know this and I would hope it would push teachers to be the best they can be. I know I am going to keep that thought in mind as I am planning from here on out.

Effective Instruction
Larson then went into what makes effective instruction - things that result in improved student learning. He referred to them at T^2 - Tasks and Talk. Tasks include conceptual engagement and productive struggle. The single most important thing we do is to focus students on learning mathematics. We use too many low level tasks and we need to do high level tasks that include discussion, comparing, etc. The assessments that are coming will have many more high level tasks he believes. All too often in the US, the classroom is a place where students go to watch teachers work.

As far as productive struggle, we need to understand that when we tell students how to do it - we take away their ability to think and disengage them. We need to allow students to productively struggle. (my emphasis) We send the message that every problem can be solved in 30 seconds or less and that is not reality. It takes more time and students need more time. We should be asking students to engage them. When they don't know where to start, ask "What did we do today? What did we do yesterday? How are they connected?"

The CCSS and NCTM share a vision that it's not just about the content, but about the process. The first three Standards of Mathematical Practice relate back to the NCTM Communication standards. He recommended reading the NCTM Book Making it Happen which I had already gotten earlier at conference, so I guess this moves up on my reading list. Larson also reminded us that 44 states have signed on to CCSS which means they have signed on that we should be teaching both content and process.

The research Larson did shows that when mathematical discourse occurs in the classroom that student achievement is higher. If you listen to the nature of classroom conversation during a lesson, if it's primarily the teacher, it's not good for the students. How the conversation is structured is more important than what the conversation is about. There are three classroom mantras he suggested:
How do you know?
Can you explain?
When a student responds to a question, you should follow up with one (or more) of these questions. He even suggested we post them in the back of our classrooms so that as we are teaching we see them and remember to use them. Students need to have that understanding. We should plan questions we are going to ask during a lesson. Important for students to be able to explain how to do #12, not what the answer to #12 is.

School Organization to Support Learners
Myth - There is too much time spent on assessment. Larson feels we spend too much time on the wrong kind of assessment. Our state tests are like autopsies - they're done after we can do anything about it. We don't spend enough time on short diagnostic ongoing assessment.

When students struggle we do one of two things -
Slow it down (so we don't cover all the material) or
Speed it up (so we don't cover the material well).
Struggling students if given enough time can perform as well as high performing students. Too often schools serving large populations of minority students emphasize "slowing down" instead of learning the content well. We end up taking students who need the most content and give them the least. (my emphasis) Larson calls this Educide by the Low-Slow Math Group. 85% of the students placed in the low group are still there when they leave school.

Larson advocated doing Formative Assessment, especially K-8, at least weekly. It needs to be done by all grade level teachers and graded consistently (all 8th grade teachers give the same assessments and grade the same way). Teachers should have the same level of expectation across grade levels as well. Intervention needs to be done in addition to regular instruction. All kids are expected to have the same content and it is important to get them additional help to get them where they need to be. So, after (weekly) assessment, there should be additional intervention outside of class. In middle school and high school, call it a Math Seminar. Provide additional intervention there with more instruction, more guided practice, more scaffolding, and more support.

Time and support must become variables. Some students will require more time to learn and so the school must develop strategies to handle this. Time needs to be variable so that learning becomes fixed rather than time being fixed which results in the learning being variable.

In Japan, grades 1 and 2 are primarily math and reading. There is no time given to science or social studies. They get that it's all about having a good foundation in reading and math. The early elementary years are key - if we get students on track in grades 1 and 2, it makes a significant difference in how they do the rest of the way through school. When everyone is taking the same course, there is no achievement gap. (emphasis mine)

The best predictor of how a student will do in college is how high of a math class a student takes in high school. But, by the time a student arrives at HS, their path is already chosen for them. Larson feels that the future of the society we live in depends more than ever on reaching all students. If students are well educated, they will have good skills and be able to get good jobs. If students are not well educated, they will end up in the service economy. We no longer have good manufacturing jobs for students who are not well educated. We have an obligation to educate our children - they don't have opportunities in their lives otherwise.

Remember it's not what you say, it's what people hear. Drug companies know this. They don't provide "treatment" but "prevention" or "wellness" instead. If we say we have an "achievement gap," people hear that it's the students' fault. If we call it an "instructional gap" instead, it puts some of the onus on us. It's not that we have intentionally done this, but it does exist because of what we have done. We have had the failure to have the will to do what we know makes a difference.

This session was very powerful for me. Of the CCSS sessions I went to, it was the one that left me with the feeling that I could do something about this in my own classroom and district. It helped put together for me why it is important that I bring in rich problems into my classroom. It clarified for me why what I am doing in my classroom is not the best thing for my students. I've known that but I haven't felt like I've known what to do about it. I think I know where to go from here. Now I just have to figure out where to start. I have a lot of things to start researching and reading about and I think it will also put the fire under me to get really reading the blogs and being back on twitter trying to exchange ideas and get going in the right direction.

Friday, April 15, 2011

NCTM11 - Common Core

I went to three different sessions today about Common Core.  Two of the three sessions I was at were packed solid - the third was in Hall F and wasn't anywhere near as packed. This is definitely one of the things teachers want to know about this year - or at least it seems that way by the attendance at sessions on Common Core.

I started off at Learning Progressions and the Common Core State Standards that was done by Bradford Findell of the Ohio Department of Education. Of the three sessions, this was the one I got the least out of and I left it early to head to stop at the exhibits before heading to see Arne Duncan speak. Friday was my most solid day of sessions. Most of what Findell talked about I already knew - he reviewed the nomenclature and organziation of the Common Core State Standards (CCSS - which corrected to CUSS the first time I tweeted from my phone and I thought that was amusing and telling).

Most of Findell's presentation was on the progressions - sequence of increasing sophistication in understanding and skill within an area of study. The first he touched upon was the Learning Progression - how learning grows in an area. This is based on research on student learning. He spent the least amount of time on this progression.

The second progression is the Standards Progression - analyzing where kids are supposed to come from and are headed. This is built into the standards. CCSS Math does not support this easily, however there are standards progressions that are being put out by the CCSS writers here and it is written by Bill McCallum (see info later on). Ohio and some states also have done Standards Progressions and you can find Ohio's CCSS resources here.

The third progression is Task Progression and Findell spent the most time talking about this. Task Progression is afforded by tasks. A rich mathematical task can be reframed or resized to serve different mathematical goals (and the goals might lie in different domains). It also has multiple entry points. He then spent the rest of the time I was there going through a task involving a fixed area and changing perimeter.  I have seen something like this before and left after I pretty much came to the conclusion that I had seen all the new stuff I was going to out of this session.

The second Common Core session I attended was presented by William McCallum from The University of Arizona and Zalman Usiskin from The University of Chicago (and UCSMP). They split the time and presented their viewpoints on the CCSS. The video from this session can be found at the NCTM website here and you can also find the video from the Arne Duncan address/question and answer there as well.

Bill McCallum spoke first. His powerpoint is here. McCallum was on the committee that wrote the CCSS.  He began and ended his talk talking about the idea of the original 1989 NCTM standards as being a jigsaw puzzle and that the CCSS was putting the pieces of the puzzle together. He did this huge analogy to Keats' 'Ode to a Grecian Urn' that I had a really hard time following.

He then went into the design features of the CCSS. The first thing he talked about was the word "understand" and how it was in many of the standards. He did say that single standards don't take place in a single lesson or day and that any lesson can and should cover several standards. He also talked about balance but I didn't get a chance to write much on that in my notes.

McCallum did say that they needed to make decisions to get rid of the "mile wide inch deep," especially in K-8. There is less emphasis on data and more emphasis on number and operations in K-8. They also moved away from universal strands K-12 that state standards had and focused on domains with a beginning and end.

As far as high school goes, Reasoning and Sense Making is the focus. Want to focus on the application of the mathematics. Seeing structure in expressions is a theme throughout High School mathematics. They did not divide HS mathematics into courses but into themes. They also wanted to embed the NCTM process standards (originally from the 1989 doc) so they could be taken seriously. They are now the Standards for Mathematical Practice and they should be assessed. (see more on this later - 3rd CCSS presentation)

There is also coherence in CCSS - "flows" in the standards that are multi-grade. If you look at his slides, you'll see what he means and it also shows up in some of the Ohio Department of Education CCSS information. McCallum feels that mathematics comes together - it pulls things together that may seem different at first. There is also coherence in the standards since the domains are also tied together.

There are two websites he recommended: Progressions and the Illustrative Math Project. The Illustrative Math Project site is not up yet but will be shortly. Also on the list of resources were the Common Core Tools blog mentioned earlier and the NCTM sample Reasoning and Sense Making tasks.

Next up was Zalman Usiskin. He emailed me his powerpoint he used and I have it here. He started off quite quickly and you could tell he was fired up about his viewpoint on the CCSS. He started off by saying that when standards documents come without associated high stakes tests, creativity is inspired and it gives stepping off points for curricula. When standards documents come with associated high stakes tests, it is like a road with no turn offs and it stifles creativity. He implied but did not out and out say that CCSS is the latter, not the former.  Usiskin feels that CCSS is a mandated national curriculum.

He then went through several assumptions (read his powerpoint), some true, some not true in his opinion. He did make the point that in the last 20 years, we have made substantial, unprecedented gains in several measures such as the NAEP and SAT (see the powerpoint for stats). He did say that students are not the same as 20 years ago and that all indicators show that we are doing better than we were 20 years ago.

The next section of the presentation Usiskin went through (briefly) what he felt were the positive points and (in more detail) the negative points of CCSS. Take the time to read through the powerpoint to see what they are - especially the negatives that are spelled out pretty well.  The biggest ones that caught my attention was that there is a total disregard for technology K-12 and emphasis on paper and pencil and that there is an overloading of material in 6th grade. I have not looked at the CCSS K-12, only really 9-12 and those things were surprising to me. Usiskin feels that CCSS brought curricula back to a world that doesn't exist and that many algorithms are out of date.

One of his biggest concerns he expressed here was that the CCSS is being used word-for-word to develop standardized tests that will be given beginning in 2014-2015. CCSS was not developed with enough time or consideration to public reactions - they were rather rushed in his opinion. CCSS has never been tested with students anywhere either. He feels that the flaws need to be corrected - the most glaring ones immediately, the rest at a set revision (possibly beginning in 2015 for implementation in 2020). He also wants high level test created that are not destructive.

The ending of his presentation (which I ended up missing to head to another session) was his recommendations for fixing CCSS. There were six of them and they are explained in detail in his power point. This presentation from both sides was excellent and if you have the time to watch it, I would recommend it.

I had rushed out of the end of Usiskin's talk to head to a 3 pm session that wasn't what I expected. So I decided to pop in on former NCTM president Hank Kepner's talk on the NCTM Perspective on Common Core. Well, really, it's Kepner's perspectives. After having heard McCallum's and Usiskin's perspectives, I found Kepner's to be somewhat of a middle ground but leaning toward Usiskin's point of view. Kepner mentioned many "cautions" (his word) about the CCSS. I'm not going to blog about all my notes from Kepner, but I am going to hit what I feel are things that haven't already been said.

Kepner's main emphasis was on the Standards for Mathematical Practice. He even had us repeat the whole name for them several times. It is a small part of the CCSS but Kepner feels they are the most important part of them. He even made the point that the governors signed on to them as standards and may not have really realized they did that.  Basically, he was saying that the content standards aren't enough. We have to do the Standards for Mathematical Practice also. Simply teaching more mathematics content is not the answer.

We need to address students' lack of engagement. This is the greatest problem in math classrooms. Kepner reported that the most challenging problem reported by US teachers of Algebra 1 is unmotivated students. As we phase in CCSS we must include Standards of Mathematical Practice in all aspects of implementation. New curricula should include tasks addressing the Standards of Mathematical Practice and professional development systems should expand instructional strategies. Kepner also reminded us that we shouldn't just do problem solving on Fridays - we should be doing it daily.

Multiple representations are important. There are prerequisite knowledge and skills in other domains needed for student learning for progression. The example he showed was for fractions.

The success of CCSS depends on the ability of teachers to assist students in learning the specified "fewer" standards at grade level and in using them extensively in subsequent situations forever. The point Kepner was making here was that even though there are fewer standards (which we wanted), many things are only taught once and students are expected to remember them once it's been taught for the remainder of their K-12 math experience. To me, that means vertical discussions have to happen and there has to be communication as to what is being taught when. It also means that everyone has to teach what is in the CCSS or it won't work. Mr. Smith can't decide that he only has 2 years left so he's going to keep teaching what he has been for 28 years.

Kepner spent a lot of time talking about assessment. There are two consortiums that are driving the assessment on CCSS - PARCC (used to be Achieve) and Smarter Balanced Assessment Consortium.  The states are split 50-50 between them and they are not required to be members of any consortium. Kepner feels there are states that may opt out of some parts of assessments due to costs (the performance based assessments - they are expensive to grade).

Both consortiums are working on building assessment pathways to college and career readiness for all students. There will still be one test at HS as there is now and the 3rd-8th tests as now. Achieve wants end of course exams in addition, Smarter Balanced doesn't seem to be heading that way. The second thing the consortiums are diong is creating high quality assessments. PARCC is creating quarterly tests that you would give each quarter to your students. They are promising quick grading and return to teachers so that they are more useful to school. I believe that these results only go to the schools and are not reported out. Kepner's concern with this is it creates a lock step curriculum and he feels it is contradictory to CCSS. He also stated it seems to be dictate when we teach what.

Smarter Balanced also is looking at the same idea but instead of them being 1st quarter, 2nd quarter, etc, they would have modules around key topics for "quarterly" assessments.

PARCC also has in its plans to create model instructional units and content frameworks. This really concerned Kepner because the assessors would be creating the curricula and he didn't feel that was good.

As far as high school and the CCSS, there is a substantive need to unpack many of the standards to clarify how sub-constructs develop and build. CCSS is weak on getting students to be career ready. Kepner also talked about Appendix A. It is in the document, but not in the document. It was done very quickly. Kepner told us it is not mandated. I added the bold here because I think states and subsequently high school teachers are treating it as such. Appendix A is examples and we need to look at it and offer feedback to our states and CCSS. He also suggested we go back and read the Summing Up from March which talks about traditional (Alg-Geom-Alg 2) versus integrated possibilities.

Kepner feels that the pathways lists are not as important as the focus, the coherence, and the connections(his emphasis) that support a student's learning and mathematical maturity. We need to look at how the ideas are developed and do it thoughtfully. We should also include a strategic use of technology. Kepner said the CCSS are silent on technology due to political debates and that we need to incorporate technology. We need to find enriching tasks that use technology in part.

The last concerns that Kepner expressed were for the high performing (gifted) and the low performing (special needs) kids. He is afraid that the high performing kids will get missed or lost. It's not like you can just move them ahead a grade level in math and then expect them to test for their own grade. And as far as the struggling students, we have lost some of the time for development since CCSS does many things once.

Whew! That was a lot but I was glad I went to the sessions. It gave me a better perspective on how CCSS was developed and some of the issues that go along with it. I now also have a better appreciation of how CCSS ties in with what NCTM has done since 1989 (which has encompassed my entire teaching career). I am still not sure where I stand on the CCSS, but like it or not, I have to teach under it. I have to make it work as best I can. And when I get back to my school, I have to get the word out that we have to all make it work. That may be a challenge, especially at the high school end. We shall see.

NCTM11 - Differentiating the Math Classroom to Engage All Students

First session Friday morning bright and early at 8 am was New Perspectives: Differentiating the Math Classroom to Engage All Studentss by Nanci Smith. All of her files are found here and the relevant ones are NCTM, Profile Assessments for Cards, Profile Assessment Word, Observation Forms, and Kid Friendly. Nanci was the first (and only one at this point) speaker to immediately give us a website where her information from today's presentation was. So far, everyone else has either had packets, given an email to request electronic form of said packet or not given any information except maybe an email at some point during the presentation.  Last night we were lamenting that NCTM really needs to get with the times and have presenters have information available to attendees electronically. But, I digress...

These are my notes from Nanci's presentation this morning. I highly recommend you go to her website and look at her NCTM file. She had an hour and stuck to it and because of the time constraint, there were many things she went through quickly that I don't have great notes on. I would have gladly listened to her for an hour and a half and it would have been even better if NCTM would have let her do the gallery workshop she would have preferred to do.

As math educators, we want math to be
**understandable  (clairify the curriculum)
**appropriately challenging
The last two can be covered with differentiation.

We need to differentiate in three ways -
**Readiness - want maximum growth with appropriate challenge
**Interest - motivation (all kids have different ones)
**Learning Profile - how do brains function NOT learning styles. This is the most efficient way to teach students - there is no reteach even though it may take no time.

She did mention Understanding by Design which is on my summer list of things to check out.

Dissect into three parts:
Know - facts, formulas, vocab, "how to"
Understand - big ideas (what makes math math and not arithmetic), concepts, strands through units/grades, mathematics v. arithmetic. These are in sentences in her classroom
Able to Do - skills, transfer, evidence - As a result of knowing and understanding I can...

Closure is important - at minimum have students share with a neighbor how they better understand the big idea of the day and then have a couple share out their discussion.

Understanding math includes but does not mean number crunching. She then went through a development of addition and subtraction from whole numbers all the way through Calculus. The overarching idea she talked about is that you can only add or subtract things that are alike. And if the things are not alike, is there a way to make them alike so you can add or subtract them. Seeing this really hit that home with me.

Appropriately Challenging
**is like one size fits all clothing (it doesn't, and not everything we do fits every kid)
**look at the whole picture - the journey is often winding and you need to find the entry point (back to readiness) relative to a particular understanding or skill

The appropriate challenge is 10-15% from where they are when they start. How do you measure that??? The next step from where the student is at is where to begin.

If you only differentiate by readiness - you will be tracking your students (don't want to do that!).

**students are all over the place
**how do I structure lessons for different entry points?
Nanci then proceeded to put up a slide that had three different color groups (green, red, blue) and a list of activities the group was to be working on to develop their understanding of adding fractions. The assessment or homework activity - not really sure which because she was flying and I was trying to keep up with my notes was also listed.  This slide is in her presentation - take a look at it to get the details. The biggest thing I got lost with in here is how to implement it. I've never done anything like this in my classroom. If I have three groups (or more), I can't be with all of them at once. And I don't necessarily want to start with the lowest group first because that might call attention to them and I don't want that either (although I suppose if the classroom culture was welcoming and open, etc. like it's supposed to be when you use rich problems so that students feel welcome to mess up it wouldn't be an issue). How do determine where to be first and get them going, while still being "less helpful?" Still working on figuring that out.

She also talked about using two columns for notes among other ways. Her method was based on Cornell notes and I really liked that she had on the Model side everything spelled out and then left the kids to go on their own on the other column. Still trying to figure out whether to have the paper in front of them like the screen with everything written out for them with hints or to just have it on the smartboard for them to copy. But I liked the idea and will incorporate it.

Engaging (make it relevant)
If it's too hard/easy
If I'm not interested
If it makes no sense to my brain - How am I going to be engaged???  Goes back to the readiness, interest and learning profile from earlier.

She had a list of things to help make it engaging which I missed but I did catch that novelty was a great way to engage students. She talked about a couple of games that you can easily create instead of giving students worksheets so they would work through the problems. Check out the NCTM file for details.

She also mentioned Dan Meyer's TED talk and be less helpful. Her comment on it was that you are enabling students when you help them. If we aren't less helpful, kids won't be independent learners. Give them a list of questions to guide them. I felt this directly tied back to the Productive Struggle session from yesterday.

The last major thing she talked about were Learning Profile cards. Learning profile refers to how an individual learns best - most efficiently and effectively. She has a learning profile card on the website as well as some other files that I referenced earlier that are related. Again, I was having trouble keeping up and at this point the session was almost done so she was really flying through stuff. The learning profile cards help to assign students to groups by how they learn. As part of the presentation she listed the top three reasons for using the learning profile cards. The #1 reason was to create a community of learners. Definitely something I want. Her main point with the learning profile cards was "How can I help you best if I teach you all the same way?" Gardner's Multiple Intelligences and Robert Sternberg's Intelligences (which I had not heard of before) are a part of this.

The last few minutes were sharing some activities using differentiation (also part of the slides). I really felt this session was valuable and had a lot for me to think about. This gets added to the summer list for exploration as well.

Thursday, April 14, 2011

NCTM11 - Supporting Productive Struggling

My 2nd Session (Thursday) was done by Susan May and Kathi Cook from the Charles A. Dana Center at the University of Texas (Austin). I also met up with @Fouss and @Sarah_IC - all three of us had it on our list.  I chose this one because I have lower level students who do struggle and I don't want them to give up so easily.

Website with more information - in progress, presentation and handouts will be there eventually.

The first part of the session was spent talking about what persistence is, what characteristics persistent students have and the importance of it. The second part of the session was talking about some of the mechanics (for lack of a better word) of how to get there.

Bascially, they chose to focus on Algebra 1 because it is the course that creates the greatest angst - there are two transitions occurring at that time: the transition from Middle School to High School and the transition from K-8 Math to math that has an algebraic focus.

Persistent students -
**understand the role of challenging tasks in learning
**understand that setbacks can be a natural part of learning
**engage in self-monitoring
**learn from setbacks and struggles

Persistence is related to what you're doing.

They talked about the theories of Carol Dweck (views of intellegence - fixed vs. malleable) and Barry Zimmerman (self-regulated learning theory). These theories shaped quite a bit of their work.

Why do we want to persistent learn?
**The problems get bigger.
Think of a time outside of school where you struggled. Then think of the satisfaction when you get through the struggle. This was how they framed why persistence is important.

As students are working through the problems, they have 2 tools - a Problem-Solving Tool and a self-reflection tool.  The problem solving tool has the four steps outlined with key questions - make a plan, monitor work, evaluate, and loop back. The idea is that students are jotting down their thoughts as they work through the problem. Then, once they are finished, they complete the self-reflection tool, which is a series of questions about how the process went.

As you are working through introducing the process to students, you start with smaller, easier problems first (the bucket problem from Die Hard for example). You should be modeling what the thoughts of a persistent student are and introduce the inner dialogue to them. You have to step students into this process.  Help students to learn how to reflect and understand that it's not just about the answer. There is a delicate balance between productive struggle and frustration.

This whole process takes time.  The suggestion was to set aside a day each week to work on the problems in class (for example, Fridays). Students can work on the problems outside of class, but only that day will be devoted to class time on the problems.  They suggested the NOYCE Foundation Problems of the Month, which have 5 levels to the problems. This way, all students can find somewhere to start, but also will reach a point where they struggle.  It doesn't matter where the kids get with the problem (Level A, Level E, etc.), but it matters that they are struggling.  Every student is working at the place they are at. It's important to make srue they are reflecting. The ultimate goal is that every time they are working on challenging problems students are asking themselves the reflective questions.

Two other websites they provided:
Academic Youth Development
Neuroscience for Kids

I really liked this session. I am still struggling with the how to make the Rich Problem thing work and for the first time, I felt like I had an answer on how to start. I definitely want to incorporate this in my classes next year. This will be a definitely project to pursue this summer. I am also considering incorporating this into my Math 1 classes for the rest of the year just to see how it goes. Haven't decided if I'm going to for sure, but I am thinking about it.  Good session - check out the websites.

NCTM11 - Teaching for Reasoning and Sense Making

The first session I attended at NCTM was "Teaching for Reasoning and Sense Making: How Does it Work?" and Fred Dillon, Jenny Salls, and Christine Thomas were the presenters.  I have seen Fred Dillon before and that was part of the reason I chose the session. The other reason I chose it was because the title intrigued me. The pdf of the slides for this session can be found here.

Basically what reasoning and sense making does is puts the mathematical skills into practice.  It fits right in with Race to the Top and the Common Core  practices.  I think I remember Fred saying that this really fits in with the first one on the list.

We proceeded to work through a problem about fish dying off in a lake and the lake being restocked each year and we were to figure out how many fish were in the lake at the start of the 2nd, 3rd, and 10th years and when it reached zero. Fred had taken a "typical" problem from a textbook and modified it to this. The problems that Fred talked about creating (like this one) have multiple entry points and can be done arithmetically and have multiple representations. There were five he listed but I didn't get them all written before the slide went off the screen. Three of them are Algebraic Formula, Graph, and Table.

The biggest problem that we have as teachers is when we tell students we will help them with the first step or tell them how to figure it out step by step.  We need to let the students struggle, for we are not really helping them by telling them what to do. (see more on this in my next post on my 2nd session).

As students are working through the problem and asking questions, things to think about include "How do we handle this? Does it matter?" (at the time it was in reference to decimal values). The most important thing to do is try it and see - encourage students to explore and not to worry about mistakes.

Fred also mentioned that other similar type problems to this one could include compound interest, exponential decay, and half-life of medicines. Once students have completed this type of problem once, you can consider these related problems to see how they can apply their reasoning to similar, but differing situations.

Some other thoughts from what Fred had to say include:
Reasoning and sense making should occur every day. I can see this - it is the main part of math (non-content wise) that can help our students do well beyond schooling.

Reasoning and sense making is NOT a list of topics to be covered.

I have a note about "productive ways of thinking that have become customary" but I have no idea why that is there.

Things that should happen as a part of Reasoning and Sense Making:
**Good Questioning Techniques
**Adequate wait time (and we never give enough of it - we think it's 30 seconds and it's only been 10)
**Resist the urge to tell students everything

How can you get started?
**Recast the material as questions. The opening problem was a typical textbook example.

The other two speakers walked through examples with finding x- and y- intercepts, graphing linear equations, and difference of squares (factoring).

Here's where I am at with this sesssion -
Great topic.  I needed to hear this.  I need help in how to make it happen in my classroom. I picked up 3 of the Reasoning and Sense Making books from NCTM (25% discount yay!) and they move to my reading list.

But I need to learn how to be less helpful.  I know we've talked about this in the math blogosphere and I probably need to search through Dan Meyer's blog to find it. Anyone else have suggestions on how to be less helpful and how to do these types of problems?

Here's the other thing - I still don't get how I am supposed to handle covering the content I am supposed to in my class. When does the teaching go on? Or do the kids figure it out from the problems? How does this all work? I guess that's my biggest issue on "rich problems." I think they're great, but how do I incorporate them into class and still get the content covered that I'm supposed to? Do any of my readers have any insight into this or know of someone who has blogged about it? Any and all help is appreciated.

Tuesday, April 05, 2011

Time to Start Rethinking

I am going to work on trying to blog more in shorter bursts. I guess I have tended to use this to think out loud and I have lots of stuff running around in my head.  Now that we have (finally!) gotten into the 4th nine weeks - I am starting to get caught up, just in time to head to NCTM next week in Indianapolis.  However, I have some stuff running around in my head I need to get out and if my dear readers will indulge me with some comments, I would appreciate it.

I started doing feedback problems with my Algebra 2 students at the beginning of the 3rd nine weeks after the whole midterm debacle. Basically there is a problem on the SMART Board when they come in and they work it out and hand it in. I go over the problem with them in class and write comments on their paper and hand it back the next day. I think it's worked okay - the students are engaged when they come in. I kind of get an idea of where they are at, although they tend to work on them with help rather than just on their own. I haven't decided if that's a bad thing or not. I have seen some excellent peer tutoring through the problems. Some students every day need help (some because they just have no clue and others have no clue because they didn't pay attention). It does force them to do a problem every day and that is a good thing. They still aren't doing their homework like they should and that still remains an issue.

I think I may incorporate this into my Math 1 classes next year. They definitely aren't doing their homework. I think the core issue for both classes is how do I get the students to practice problems when I am not grading them for homework. Someone had suggested in the comments of my last blog post they were having the same issue and maybe the answer becomes incorporating more in class problems. I think my students have no clue how to take notes in math class as well and, well, that's another issue I want to deal with next year.

If you aren't grading homework, how do you get students motivated to work through problems? How do you teach "note taking" in a math class? Does anyone have any good resources for either? Again, I am mostly thinking out loud here and making some notes for summer of things to work through. Thanks for your thoughts and taking the time to read this. :-)