Abstract
The study explored the verb clauses and thematic development evident in curriculum materials and in transcripts of teachers planning lessons using the materials. A central argument is that though teacher characteristics influence the ways they plan lessons with curriculum materials, the materials themselves influence teachers’ planned lessons via the ways mathematics is construed in the materials. We used verb clause and thematic analysis to analyze the features of curriculum materials and teachers’ lesson planning using those materials. We found differences between the curriculum materials in terms of how they construed mathematical activity and found that teachers’ lesson plans roughly aligned with the features in the materials; this speaks to the impact of features of curriculum materials on teachers’ lesson planning. We also found small but perceptible differences between teachers from different curriculum backgrounds, suggesting an enculturating effect from the materials.
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This research was funded in part by NSF grant DRL 1222359.
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Appendices
Appendix A: Directions for planning the lesson (staged lesson plan)
You are going to be asked about how you would plan a hypothetical lesson using the materials we provide to you. In the interview, we will ask you questions about the lesson you planned and about how the resources (e.g., student text, teacher resources materials, standards, sample assessment items) contributed to your planning. Try to plan the lesson as much as possible with the materials provided, while working in a way that is typical/representative of your usual planning practices and aligned with your approaches for teaching and learning. It will be helpful if you invent a hypothetical group of students who would be the intended audience of the lesson. This will help ground your lesson planning and provide us information about your instructional goals. We are going to ask you specific questions about your lesson, so it would helpful to at least sketch out an agenda of activities that would constitute the lesson.
Appendix B: Semistructured protocol for lesson planning with regular materials
2.1 Instructions to observer
This is an observation of a teacher planning a lesson with opportunities for you to probe the teacher’s processes and rationales. It is important to stress that this is not an evaluation of the teacher’s planning or how the teacher uses particular resources. Try to maintain a positive though inquisitive tone to avoid having the teacher feel as though he or she is being evaluated. We are particularly interested in how the teachers access and interpret the teacher resource materials.
One way to begin the interview is to have the teacher think of you as a student teacher who needs to understand how the teacher plans. Additional probes for some of the questions are written in italics. If possible, video record the observation, with attention paid to capturing images of key artifacts using the ‘photo’ feature of the video camera.
Below is a list of topics that might be mentioned during the observation. Please use the attached form to check off those items that are discussed and to generate a narrative of the planning session. The video or audio recording will be analyzed again later, but we want to generate an initial description of what happened.
Background characteristics

Participant

What grade levels have you taught? What grade level are you currently teaching?

How many years of teaching experience do you have?

How often have you taught this particular lesson?

Questions about lesson organization/flow:

1.
How will you introduce the lesson?

2.
What will you ask students to do during the lesson?
Interviewer: Probe for the presence/absence/nature of the following:

a.
Exploration

b.
Practice

c.
Group work

d.
Discussion

a.

3.
What materials will students have access to (worksheets, textbook, overhead display)?

4.
How will you close the lesson?
Goals and purposes of the lesson

1.
How does the lesson address the CCSSM, in terms of:

(a)
Content standards?

(b)
Standards for mathematical practices?

(a)

2.
How does the lesson fit into your district’s sequence and pacing guidelines? (i.e., What content precedes and follows this lesson? OR What leads up to this and what does this lead to?)

3.
Do you have a set of guiding questions that you will use during the lesson to probe their mathematical thinking?

4.
What are the goals for the lesson? [what do you want students to walk away with from the lesson?]

5.
What kinds of challenges [where will students struggle procedurally or conceptually] and strategies do you anticipate?

6.
In what ways do you see this lesson aligned with your interpretation of the intent of the CCSSM?

7.
How does the lesson address:

(a)
Use of and connections among representations?

(b)
Anticipated student strengths and weaknesses?

(a)
Questions about resources that were accessed to plan the lesson

1.
What documents/ texts did you use to plan the lesson?

2.
Which part of the teacher resources from the curriculum materials did you consult when planning this lesson?

3.
Can you show the pages or websites that you looked at and describe how you drew from those pages/websites?

4.
What other information or resources would you have liked to have in order to plan your lesson?

5.
How do the student text materials address the learning needs of your students?
Probe for presence/absence/nature of the following:

(a)
students’ prior learning,

(b)
students’ backgrounds and experiences (e.g., family, culture, language, community),

(c)
students’ strengths, and

(d)
potential difficulties?

(a)

6.
Did you adapt or revise these materials for use in your classroom? Why?

7.
How do the teacher resource materials help you to understand:

(a)
The learning goals for the lesson?

(b)
The mathematical content of the lesson?

(c)
The sequencing of the activities in the lesson?

(d)
The organization/structure of the main activity in the lesson?

(e)
Important questions to ask students during the lesson?

(f)
Anticipated student strengths and difficulties?

(g)
Group work strategies?

(h)
The resources you need to provide students during the lesson?

(i)
Ways to adapt or revise the materials to meet your students’ needs?

(a)
Appendix C: Staged lesson planning interview protocol
Staged lesson planning
Individual teacher planning interview protocol
3.1 Instructions to observer
This is an observation of a teacher planning a lesson with materials that are different than what they typically use. The teacher has been given the materials about a week in advance of the interview and asked to outline a lesson. During the interview, you will ask questions about the design of the lesson and how the teacher used the materials provided to them. The intent of the interview is to develop a fuller understanding of the teacher’s perceptions of curriculum materials with respect to CCSSMrelated goals.
Set up the camera so that you look over the teacher’s shoulder to capture their gestures and so that you can see the artifacts to which the teacher is looking or referring. The best angle is probably over the shoulder of the teacher, pointing down so that you can see the teacher’s face and hands as well as the planning artifacts.
Begin the interview by asking the teacher to describe the context for the lesson, as indicated below. Then, proceed through each section of the protocol. It’s okay to skip questions if the teacher has already discussed the topic in detail. When in doubt, ask the question even though the teacher may have discussed it.
Ask teachers to point to where they are reading/skimming as they go through materials and “think aloud” as they go through the materials and “read aloud” any sections that they are looking at closely.
3.2 Interview protocol
Design and content of lesson

1.
Describe the class for which you would teach this lesson (e.g., grade, prior mathematical achievement, size of class). You can use a current or past class as a context in which to situate your planned lesson.

2.
What is the primary content of the lesson? [Prompt for evidence for their claims]

(a)
To what extent is the content appropriate for your students’ mathematics knowledge and understandings?

(i)
If it is not appropriate, ask: In what ways is it not appropriate and how (if at all) could you adapt the lesson to better fit with your students?

(i)

(a)

3.
What Standards for Mathematical Content are addressed by the materials and where/how do you see them addressed?

(a)
To what extent does the content align with (your interpretation of) what you need to teach for the CCSSM?

(i)
If it does not align, ask: How (if at all) could you adapt the lesson to better align with the CCSSM?

(i)

(a)

4.
What Standards for Mathematical Practices are addressed by the materials and where/how do you see them addressed? [See attached list of standards for the given topic]

5.
Describe a lesson from start to finish. [Interviewer probes for components and characteristics of the lesson, as necessary].

(a)
How would you start the lesson?

(b)
How would you introduce the topic?

(c)
What kinds of problems would the students work on?

(d)
What activity structures would you use, and what are the goals for each type (e.g., what do you hope to accomplish in a whole class discussion)?

(i)
whole class lecture,

(ii)
whole class discussion,

(iii)
small group work,

(iv)
independent seat work

(v)
something else (pair work, pair consultation during independent work, etc.)

(i)

(e)
What kinds of student reasoning/ student strategies/ student misconceptions would you anticipate?

(f)
How would you address or respond to the challenges and anticipated student reasoning?

(g)
How would you informally assess your students during the lesson? What are indicators of learning or needs that you would look for?

(h)
How would you conclude the lesson?

(a)

6.
Now we are going to ask you about the ways that the lesson activities develop student reasoning over time. We are going to prompt you to explain the connections or progressions across the different parts of the lesson.

(a)
How do you see the activities you described as being connected to one another? Can you describe how the activities are intended to progressively build students’ understanding of the topic? What kind of connections or progressions do you see across the activities in terms of helping students understand the main goals?

(i)
E.g., demonstrating, guided practice, independent practice

(ii)
E.g., introduction to concept or task, problem solving, summary discussion

(iii)
Other?

(i)

(b)
How is conceptual understanding developed across the lesson?

(c)
How is procedural fluency developed across the lesson?

(d)
How is language or terminology developed across the lesson?
Teacher resources

(a)

7.
How do the teacher resources help a teacher to understand (be specific in pointing to or identifying the passages for each):

(a)
The kinds of student experiences that were intended by the designers

(b)
The underlying mathematical concepts

(c)
How students’ mathematical understanding develops across the lesson activities [Probe on what is meant by understanding]

(d)
How students’ mathematical language develops across lesson activities

(e)
The multiple ways to represent the concepts

(f)
How the materials connect the concepts to students’ lives/experiences/past math understandings

(g)
The multiple ways students might solve or approach the problems

(h)
How to help students develop procedural fluency related to unit rates [Probe on what is meant by fluency]

(a)

8.
What are the strengths and limitations, in terms of:

(a)
The student pages

(i)
Activities

(ii)
Examples

(iii)
Explanations

(i)

b.
The teacher resource pages

(i)
explanation of goals

(ii)
explanations of how to structure activity or practice)

(iii)
ideas to support anticipating students’ thinking, approaches, and/or potential confusions.

(i)

(c)
Assessment materials/resources

(d)
Explaining how the materials address different features of the CCSSM

(a)

9.
There may be some teacher resources you’d like to consult that are not available with these materials. If so, what other resources would you find helpful? What important information do you think they would provide for you to understand these materials or how to use the materials?”
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Choppin, J., Davis, J., McDuffie, A.R. et al. Influence of features of curriculum materials on the planned curriculum. ZDM Mathematics Education 53, 1249–1263 (2021). https://doi.org/10.1007/s11858021013057
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DOI: https://doi.org/10.1007/s11858021013057