I’d like to know more about the “framework” that the first teacher talked about. What is it?
Great question, the framework that our teachers is referring to is the idea of how to present tasks in the classroom and begin to piece together students reasoning and understanding. One large piece of this had to do with finding an entry point for all of her students to be able to make sense of the problems being presented. She is also referring to the use of justification and generalization in the classroom. After doing a lot of the MMRE PD sessions she knew what that looks like in the classroom and how to support her students in reasoning mathematically.
There are a couple “frameworks” that the first teacher might be referring to. Teachers learned to identify mathematical claims that are central to a given lesson, and from this, recognize opportunities to elicit student-voiced generalizations or justifications. Also, teachers learned about the 5 Practices for Orchestrating Productive Mathematics Discussions by Smith and Stein, which then gave them a framework for organizing whole-class discussion and managing student contributions. Finally, teachers also learned about the Cognitive Demand framework, which gave them a framework to consider tasks and how they could be implemented appropriately. The teacher is probably referring to one, or some combination of all of these frameworks.
This is intriguing, but like James Madden I really want to hear a bit more! Here are a couple of questions:
1. What age.grade level are you targeting? If its’ more than one level, have you found different challenges as the math gets more challenging (e.g. if moving to algebra in 8th grade)?
2. Cognitive Demand. This is an approach which, as far as I understand it, should be used a lot more than it is. Can you give some idea of how you use it with the teachers (e.g. do you give them rubrics for evaluating tasks, or comparing different ways of doing the same task)? Is there a particular approach to this that you’ve adopted— or maybe developed yourselves?
3. I see that the project was funded some years ago – is it now well rooted in the districts you’ve worked with? Spread to new teachers?
1. We are focused on grades 4-12. While the content does increase in complexity and it becomes more difficult to find rich tasks for the higher grade levels the biggest challenge has been getting other teachers beyond the project at the higher grade levels interested in making changes to their classrooms. We ask that our teacher leaders do professional development that they have designed with the help of the MMRE team and implement it in their own schools. Unfortunately, we have found that the high school and some middle school teachers have a difficult time getting their other team members interested in participating in the PD that they are doing. They also seem to show little interest in making changes in their classrooms at all. Overall the elementary teachers have been very receptive, and of course most of the willingness to participate stems from support from the district.
2. We do not have a specific rubric that we ask the teachers to use to evaluate the tasks that they give students. However, we do have an extended rubric, and collapsed rubric that we use as evaluators when we visit the classroom. These teachers have had a lot of training with the rubric and what higher-level justification and generalization looks like in the classroom. We ask the teachers to keep this in mind as they are introducing tasks to their students and working through the problem presented to their students.
3. It has been 5 years since the project began with 3 cohorts of teachers cycling through. The first group of teachers (Cohort 1) have been involved for 5 years and a majority of the districts involved from cohort 1 we have seen a lot of change in the district where there has not been a lot of turnover. Of course there are some district that once the regional meetings (usually 3 times a year) and summer institutes (3 weeks in the summer) stopped for their Cohort we did not see as much change with the district and new teachers in the district. Cohort 3 has been involved for 3 years and they have been doing amazing work with the professional development in their district and we have seen a lot of change with the teachers within this district.
Thank you so much for your insightful questions and if you have anymore please ask.
If I can tack on my thoughts to these excellent questions as well:
1) The elementary teachers have generally been the most responsive and demonstrated the most “success stories.” Many of them had a lot of room for improvement in their math content knowledge and benefited immensely from our PD work with them. They also seemed the most willing to make changes to their practice.
2. During one summer institute, we did talk about tasks with our teachers and compared/contrasted low and high level tasks. But, like Brittany said, most of our focus has been on our justification rubric. This rubric distinguishes different levels of justification: appeal to authority, empirical or perceptual justifications (appealing to examples or the appearance of something), and justifications that appeal to a mathematical basis, and for general claims, justifications that specifically articulate why the general property will hold for all cases in the domain. We’ve found that focusing on justifications has helped to shift teachers’ focus from the task itself to how they are implementing the task. In other words, a potentially rich task can implemented in such a way that no higher-level justifications are made, or a seemingly low-level task can be implemented so as to create opportunities for a higher-level justification. The goal of our project is not for teachers to select rich, complex tasks per se, but to try to implement all tasks (regardless of scale and complexity) in a way that allows for high-level justifications to be made.
3) Spreading the project’s influence throughout schools has been difficult. As Brittany has mentioned, some of our teachers’ colleagues simply aren’t interested and have shown resistance. But perhaps the larger issue has been administrative turnover. In several districts, we’ve had very supportive administrators leave, and the new administrators aren’t as supportive. This has been challenging because such things are beyond our control.
Anyways, hope this helps clarify things further. Thanks for your interest!
Awesome to see how clearly excited these teachers are about how much they have learned through the program! Do you plan to measure student outcomes in math achievement as well?
Yes! We have been giving student reasoning assessments from the beginning of the project for students in grades 6 and 8. These are given at the beginning of the year and the end of the year. We will be grading these this summer and we hope to see how student reasoning has changed throughout the school year while participating in a classroom that has reasoning rooted in the content. We are also assessing the change in students attitudes throughout the school year.
Great program! You mentioned above about the difficulty to spread the strategies within schools to other teachers. How did you recruit the original teachers to participate?
We first talked to administrators in targeted districts (targeted by looking at rural, low SES schools). We explained our vision, and asked for their recommendations for teachers with “leadership potential.” They did not necessarily have to be leaders already, just that we needed to know they had that capacity, were well regarded by their peers, etc. For the most part, we got very qualified teachers. We emphasized that we wanted teachers with 5+ years’ experience in the classroom.
A few districts sent us their “fixer uppers” but not many. We then held a meeting with these identified TLs and again explained our vision, and went from there. We had a few teachers say they weren’t interested or couldn’t commit to the time involved, but most of them signed up.
This answer was submitted by Libby Knott (PI on the project)
What a difference you’ve made in these classrooms! Where do these rich mathematics tasks come from? Do teachers create them? Do you provide them?
We do not have any one single source for rich tasks. Rather, we draw from many paper and web-based resources. Shell Centre, Illuminations, Nrichmath, etc., to name just a few.
After a few years though we began to realize that the teachers were hung up on the rich task idea, and felt that they needed to find the “holy grail” of rich tasks. We tried to work with them to see that they could make rich tasks out of their own curriculum. At this point we began to speak of “rich implementation of tasks” rather than the tasks themselves being rich, so that teachers would begin to understand that they had the power and resources to do this themselves. We devised a method called “turning a task upside down” which consisted of taking a traditional textbook sequence, where the objective was spelled out, often a formula or procedure was provided (with little explanation or motivation for where it came from), followed by a number of practice problems, and turning it on its head. This was done by identifying the object of the lesson or activity, devising a sequence of activities (a string perhaps, or…) that the students could engage in and would ultimately lead THEM to coming up with the formula, procedure, etc. That way students would understand where it came from and why it worked.
As answered by Libby Knott (PI on the project)
How did you all track the way the lessons went during the school year, after attending the summer workshops? It is great to see the dialogue between the research and development team and the teachers who participated. I think telling more about the structure they mention, the framework, will be helpful in the broader literature. Thanks!
We visited the schools twice during the school year which gave us a snapshot into our teacher leader classrooms as well as other teachers in the school. Also we asked teachers to report during regional meetings during the school year on specific lesson development that we had worked with the teachers on and asked teachers to create during the summer workshops or other meetings. We gave our Teacher Leaders assignments which often included videoing a lesson, reflecting on a lesson, and if applicable turning in student work.
Thank you for your positve feedback and question!
Further posting is closed as the showcase has ended.
A description and overview of what MMRE is and how participants have been involved and changes to their teaching.
Copyright 2017 TERC
Funded by NSF