NSF Awards: 1119163
2017 (see original presentation & discussion)
Grades 6-8, Grades 9-12
This video will showcase the work of the Implementing the Mathematical Practice Standards project in developing and testing a robust model of professional development that supports middle and high school teachers in building their awareness and understanding of the Common Core's Standards for Mathematical Practice. The model has been tested nationally and revised iteratively with 3 cohorts of mathematics educators. Our field tests have demonstrated significant differences for participating teachers when compared to non-participants in similar schools. The PD program will soon be available for wider use through facilitator and support materials being prepared for publication in collaboration with the National Council of Teachers of Mathematics. Interpreting the Standards for Mathematical Practice will be a 20-hour course for teachers of grades 5–10 mathematics, designed to provide mathematics educators with a variety of mathematical learning experiences – including doing mathematics with colleagues, analyzing students’ mathematical thinking, and planning for instruction – that, when used together, deepen understanding of the SMP. The course draws on a set of Illustrations of the SMP designed for grades 5–10 teachers, that are centered on mathematics tasks and student dialogues that exemplify student mathematical thinking characteristic of the SMP.
Johannah Nikula
This video shares work we have been doing at EDC to develop resources that support teachers' understanding of the Standards for Mathematical Practice, and it notes the impact these resources have had for teachers. The project is in its final year and some resources described in this video are currently available at mathpractices.edc.org, while others will be available through NCTM soon. We would love to hear your thoughts about how you might use resources such as these to make an impact with teachers or leaders in your own contexts, as well as any questions you may have.
Kristen Malzahn
Given the multiple ways in which teachers currently interpret the SMPs, there is a great need for materials such as these to support their understanding of the SMPs and how to effectively promote and establish those practices in their mathematics classroom. Now that you have field tested your materials and have some data on impacts for grades 5-10, do you have any plans to expand on this work and create a similar set of materials for grades K-5?
Deborah Spencer
Deborah Spencer
Managing Project Director
It's a great question, Kristen. We do have an interest in creating a similar set of materials for K-5 and the school districts we worked with in the current project have expressed interest in a similar program for elementary school teachers. We are also big fans of the Developing Mathematical Ideas (DMI) professional development materials (written by Deborah Schifter, Virginia Bastable, and Susan Jo Russell), which support collaborative PD for teachers in grades K-8 to think about the big mathematical ideas in those grades and look at how children develop their understanding of those ideas...a new version of that program, aligned to the Common Core, is available now from NCTM http://www.nctm.org/Publications/Microsites/Dev....
Andrew Izsak
Have you found that some practices are more difficult to support than others? In our work in content courses for future middle and secondary teachers, we have noticed that some begin to reason from definitions more quickly than others. This fits under SMP3. Have you also noticed that teachers have trouble developing this practice?
Deborah Spencer
Johannah Nikula
We have definitely found that the different SMP hold different challenges for teacher understanding. For example, MP 7 (look for and make use of structure) and MP 8 (look for and express regularity in repeated reasoning) are often challenging at first to make sense of and distinguish. These two were so challenging for teachers participating in our work that we supplemented the other explorations included in the PD materials by creating a video that provides examples of each. We'll be making the final version of that video available soon. Or in cases like MP 6 (attend to precision), there can be a tendency to make assumptions based on the name alone -- e.g., mistakenly thinking that precision is just about accurate numerical answers, and therefore missing the focus on precise communication. As for MP 3 (Construct viable arguments and critique the reasoning of others) -- you make a good point about the challenge of digging into the nuances of this practice. We have noticed that with both this practice and MP 1 (Make sense of problems and persevere in solving them), there can be a tendency at first for teachers to feel like these are happening all the time (but focusing only at a surface level). So, it requires more work to help push to a greater level of specificity about what we want to see happening when engaging in MP 1 or MP 3 (e.g., as you point out -- reasoning from definitions).
Wendy Smith
Associate Director
These professional development materials are timely and should be very useful to teachers. In your piloting, did you run into situations where teachers' mathematical knowledge was lacking, and got in the way of their exploration of the practices? Did you mostly have teachers participate with others from their same school and grade level, or were the groups more mixed? Did you get push-back about any of the materials with teachers saying that their own students could not do certain things? Might there be a version of these materials that could be adapted for use with principals and other instructional facilitators who observe and evaluate math teachers but have no formal training in teaching mathematics?
Deborah Spencer
Deborah Spencer
Managing Project Director
Hi Wendy - in the field test, the materials were mostly used by teachers in same school district, or at the same school, with a few exceptions where the materials were tested in regional PD settings. We did, however, have many mixed-grade groups with middle and high school teachers participating together. We developed two versions of the PD course: one for groups of middle grades teachers, and one for groups of high school teachers; and then we developed a pathway that integrates the two versions for mixed-grades groups. We did put a lot of thought into designing both the problems that teachers engage with in the PD, as well as the structure of the PD sessions themselves, to support teachers in engaging in the mathematics themselves as learners and looking at their own mathematical thinking (as well as learning about their colleagues' approaches to mathematical thinking). Many of the mathematics tasks are low-threshold, high-ceiling problems to accommodate a range of mathematical knowledge. The PD materials do also contain student dialogues, which offer examples of mathematical thinking using three fictitious students; those dialogues are designed to be discussed as interesting exemplars, rather than representations of typical student responses -- within those discussions, we did sometimes hear that teachers considered that thinking not possible with their own students. As for your suggestion about use with principals and other facilitators -- yes, yes, yes! We would love to see a version of the materials for that audience and have put some effort into attracting funding for that work. EDC has a history of developing mathematics PD programs for administrators, through the Lenses on Learning program, and we would love to continue that work.
Libby Gerard
I would like to learn more about your PD materials. What are your thoughts on how to integrate what you have learned about PD into the curriculum materials themselves? I work in web-based materials for inquiry science and we have done some research around what kind of student work to "alert" teachers to and when, how much guidance to embed into the materials so that is valuable and not overload, how to encourage teachers use of the student work to modify practice or lessons. I'd love to hear your thoughts!
Deborah Spencer
Deborah Spencer
Managing Project Director
Hi Libby - thanks for your interest! One source of information about our work is our website, mathpractices.edc.org, which offers many of the materials included in our PD curriculum (though not the PD materials themselves, which we expect to be available from NCTM in the fall). Another source of information is our speaker presentation materials from our 2017 NCSM Annual Meeting session in San Antonio, available at ncsm.org under Session 1106 if you are an NCSM member. We also have two recent articles in NCTM journals about the Standards for Mathematical Practice: Debunking Myths about the SMP by Victor Mateas and What is "Repeated Reasoning in MP8? lead author Paul Goldenberg.
Your question about curriculum materials is a good one and I think there is a lot of potential for curriculum materials to highlight the opportunities to attend to mathematical thinking. One model for an approach to doing this in mathematics is in the new edition of the elementary program Investigations in Number, Data, and Space by TERC, in which the authors have paid careful attention to how to support teachers in thinking about children's thinking in the materials themselves. I'd highly recommend looking at their approach. From their website: "Support material for teachers—an essay about the two practices highlighted and assessed in each unit and sidebars that indicate opportunities for engaging students in all of the practices—provides images of what these practices look like in the elementary classroom, explains how math practices interact with math content, and offers guidance for helping young students learn how to use these practices in their mathematical work."
I think there is also some wonderful work going on in thinking about formative assessment in mathematics and several of my colleagues at EDC have written about this for classroom teachers, see for example Uncovering Student Thinking about Mathematics in the Common Core by Tobey and Fagan and Routines for Reasoning by Kelemanik, Lucenta, and Creighton. While not examples of curriculum per se, these books provide classroom resources and are strong examples of materials that help teachers think about supporting, soliciting, and responding to student thinking, and may be helpful models to consider.
Miriam Sherin
Professor, Associate Dean of Teacher Education
Such important work! I'm wondering how you think about the impact of the PD on teachers' instruction. One avenue would be via curriculum as you discuss above - but I'm wondering if the PD has teachers explicitly explore what a particular standard or set of standards means for their instruction, or for changing their instruction. And if this isn't explicit, do teachers report to you informally about ways they are working to align their instruction with SMP?
Deborah Spencer
Managing Project Director
Hi Miriam - in our twenty-hour PD course, we have a few different areas of focus. Specifically, the goals of the course are to:
In a subset of the PD sessions, we have teachers focus explicitly on planning at the unit and lesson level, incorporating a focus on mathematical thinking and the SMP. We also address instructional practices, including orchestrating discussions, that support the development of mathematical practice. Our focus is on helping teachers build their own understanding of the SMP and then to reflect upon their own practice and plan for modifications.
Our research on the impact of the PD course, however, was largely limited to the effects the course had on teachers awareness and understanding of the SMP and the extent to which teachers felt prepared to teach with attention to the SMP. We did not have the resources to look closely at what was happening in classrooms using for example an observational measure. Our evaluation partners at TERC did interview a subset of teachers across participating sites, many of whom did report that the PD experience had an impact on their teaching, largely in how teachers planned and enacted curriculum with students to highlight opportunities to engage in mathematical practice and enhance discussion to focus on thinking.
Miriam Sherin
Professor, Associate Dean of Teacher Education
Thanks for this information. Definitely challenging to explore impact on practice - the work you are doing so far in this area makes sense to me!
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