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 box.net 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.
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.