Changing Teaching Practices

Teacher Beliefs Card Sort (based on Swan, 2007)

Purpose: Exploration

  • What beliefs and values do we hold about mathematics teaching and learning?
  • How are they related to our practices?
  • Why do we teach the way we do?
  • Are there differences between our values and the ways we teach?

Teams were given 30 beliefs and practices statements on cards – and asked to sort them into piles of Agree, Disagree, and Cannot Decide. They were also encouraged to modify statements as needed. After sorting the cards, they created team posters of their card sorts.

Beliefs Card Sort Page 1

Beliefs Card Sort Page 2

Beliefs Card Sort Page 3

Beliefs Card Sort Page 4

Beliefs Card Sort Page 5

Teams shared how easy or difficult they found the sorting, the modifications needed, the degree to which team members agreed, and the issues that arose. They then compared their ideal values to their actual practice and looked for patterns, as well as comparing the results with their teammates.

Teachers also completed an inventory in which they estimated approximate percents of time they spend on particular types of learning activities while teaching, contrasting these percents with the amounts of time they would ideally give to each purpose.


Little Changes activity

  1. Based on the SMP, teachers were asked to imagine the ideal student in the ideal classroom – what would it look like?
  2. Teachers were asked to define 2-3 changes they would like to see in what their students do to learn so that they are closer to the ideal.
  3. Teachers considered how they could measure these changes.
  4. Teachers considered what changes they could make in their teaching in order to prompt these student changes. What one change could they initiate on Monday? How would they gather evidence of the effect of the change on their students?
  5. They were asked to share the results in November.

Student and Instructional Changes(Oct13)

November 22 follow-up activity

Teachers had sent in descriptions of changes and were grouped according to these changes: Increasing cognitive complexity, being open about mistakes, increasing student group work and discourse, or sharing student work during lessons. They shared their changes with the other teachers in their groups in a Give One, Get One activity, where they talked about what was similar or intriguing in each other’s changes. As a group they discussed what they noticed about themselves and the challenges posed and comfort level reached with making the change, as well as what they noticed about students’ responses, and evidence of whether it improved their learning or not. They then considered their change in light of the SMP-defined “ideal” student and these questions: Did their change positively affect what students did to learn (why or why not); if and how they could continue, revise, and/or change their approach to have greater effect; if and how their changed built on students’ assets; and what they thought the most important components and means of implementation were for their change.


Equitable Environments

Teachers were engaged in an activity designed to reveal stereotyped expectations. They were asked to identify characteristics they saw in students they immediately identified as likely to be successful in math class and capable of pursuing math or math-related majors and careers, including gender, socioeconomic status, race/ethnicity, extroversion/introversion, social skills, confidence, and participation in extracurricular activities, then to identify the same types of characteristics in students they immediately identified as likely to struggle and fail, then notice common themes and differences among the group members’ lists. This activity was followed by a presentation on Rosenthal and Jacobson’s (1968) Pygmalion in the Classroom study, Bourdieu’s concept of Cultural Capital, Sadker (1989, 1991, 1995, 1999) gender studies, Horn’s (2007) Fast Kids, Slow Kids, Lazy Kids study, Steele and Aronson’s (1995, 1997, etc.) stereotype threat studies, Cohen’s(1994) identification of social status in the classroom study, and the dangers of well-meaning efforts such as expressing caring in ways that restrict growth through rescuing, misused scaffolding and differentiation. Strategies were discussed that can address these issues. These strategies included methods for group formation, student training for group work and group roles; assigning competence; methods for including all students in classroom discourse, and Universal Design for Learning strategies such as multiple means of representation, action/expression, and engagement. Following this presentation, teachers were asked to individually reflect on and write steps they could take to increase all students’ active participation in their classes.


Follow-up on Individual and PLC Changes

Year 2 – June 25

Evaluation results were shared with the group regarding improvements seen in teachers’ content knowledge, pedagogical content knowledge, use of new ideas such as increasing respect for and use of students’ active participation, ideas, questions, and contributions, as well increased intellectual rigor, constructive criticism, and challenging of ideas; and improvements seen in RAMP-A schools such as higher percentages of students reaching EOC-1 and grade 8 math standards, and retaining more interest in math over the school year than in the comparison schools.

This report was followed by a description of stages in PLCs, going from learning to be a team, to coordinating common plans, lessons, assessments to collaborating to take collective responsibility for all students’ learning and designing instruction to meet all students’ needs. PLCs were asked to consider their strengths and ways they could grow that would support the PLC and each team member’s growth toward identified goals. They consider how their students might experience the PLC growth.


Follow-up Beliefs Activity – Year 2, June 26

Teachers completed the Critical Thinking Beliefs Appraisal individually as part of the project evaluation, then within their PLCs discussed their beliefs about each of the following: What lessons, activities, or tasks are appropriate for students with low/medium/high achievement, low/medium/high motivation, and low/medium/high prior knowledge. The whole group contributed to the same poster, then discussed which ideas they designed for students with high motivation, prior knowledge, or achievement would also be effective for students with low motivation, prior knowledge, or achievement.


Second Follow-up on Changes: Reflecting on Learning and Planning for Continued Growth

Year 3 -November 14

Year 2 data on RAMP-A effects were shared with the group, including positive effects on teachers’ math content and pedagogical content knowledge, instruction, and students. Teachers were asked to reflect on and write about which of these changes they had noticed, which surprised them, and how the changes were reflected in the way they thought about and conducted instruction and in their students’ responses. They were asked to identify further changes they wanted to see in their mathematical understanding, teaching practice, student behaviors and responses.


In anticipation of reading Jim Hiebert’s chapter (2013)*, The constantly underestimated challenge of improving mathematics instruction, they considered and shared reasons why improving math education might be difficult. Following this discussion, they read the Hiebert article and discussed their responses to the article.

*In K. Leatham (ed). Vital directions for mathematics education research, (pp. 45 56). New York: Springer.

Discourse For All

Year 3 – February 6

Teachers watched a video of a local math teacher describing the effects of changing his approach for calling on students so that all students were engaged in the classroom conversation, then shared ideas about how they might encourage more students to participate in their classrooms.


Year 3 – May 1

Janet discussed past project observations that teachers’ environments changed over time which seemed to interfere with continuing project learning, reminding the RAMP-A teachers that they too cannot rely on their PLC staying together or continuing to teach the same courses, or their own course assignments or administrators staying the same. However, teachers can rely on the positive effects of intentional and reflective teaching, ambitious teaching focused on all students, student reasoning, and daily assessment that informs instruction, the Standards for Mathematical Practice, and the value of peer collaboration for both teachers and students. Teachers were then asked to reflect and write individually about what they had learned in RAMP-A and their PLC work, what they had learning about collaboration, how their beliefs, goals, and instruction had changed, and what ideas and strategies they wanted to pursue but had not yet gotten to. They were asked to consider how they could continue to observe their own practice and their students’ learning, how they could maintain a routine of observing, reflecting on, and improving their practice and student learning, and how they could continually refresh their thinking about their practice. They were also asked to consider how they could initiate, maintain, and expand peer collaboration even if their PLC changed. We collected their reflections for use in the June meetings.


Follow-up to Sustainability Activity

Year 3 – June 25

Teachers read Ermeling, Hiebert, and Gallimore (May, 2015) “Best Practice:” The Enemy of Good Teaching (Educational Leadership, pp. 48-53) article, and identified what they thought the most important issues and suggestions were. They reflected together on how the article applied to them and their teaching, and, when their May Sustainability reflection was returned were asked to add specific goals and actions for their sustained learning and improvement.