Integrating a Making Experience into Mathematics Teacher Preparation Coursework
Our research has documented prospective elementary teachers’ learning of mathematics, pedagogy, and design through their Making experience and the coursework that informed it. Furthermore, we found that the development of their identities as teachers of mathematics was as central to their learning to teach mathematics as their learning of these three interrelated domains.
Looking across PMT’s design experiences, features of a pedagogy in progress were implicated, such as the following: a commitment to an inquiry pedagogy informed by constructivist principles, centering student thinking, ensuring opportunities for mathematical reasoning, teaching through problem solving, designing tasks that afford multiple solution pathways and leverage students’ funds of knowledge, and a realization of the power of toolmediated, exploratory mathematical activity.
What follows are the Course Description, Goals, and Outline from a syllabus for a course in which the Making experience was implemented. We offer this example of a course in which the Making experience was implemented in order to provide prospective users of this curriculum with a vision of how such an experience can be integrated into a course that already exists. This course is a specialized content course with some attention given also to methods of teaching. The course met for 14 weeks and for 2.5 hours each week. The course outline includes “Design Plans” that refer explicitly to components of the experience. This course curriculum is also available in PDF form here.
Mathematics Education in the Elementary School
In this course, we will explore what it means to learn and teach mathematics with understanding, and how we can help students from diverse cultural, racial, social, and linguistic backgrounds experience the joy of mathematical thinking. We will pay particular attention to how children think about mathematics and learn to use what we know about children’s thinking to design and adapt instructional activities. We will consider students’ home and communitybased experiences and how we can leverage these experiences to teach mathematics. Finally, we will discuss the roles of students and teachers in the classroom, and how to foster an equitable classroom environment that encourages rich discussion of mathematics. We will specifically address issues of power, access, diversity, and relevance in learning and teaching mathematics.
*The course draws on materials from Cognitively Guided Instruction and was largely developed by Susan Empson, PhD.
 Explore mathematics as conceptual understanding, procedural fluency, problem solving, explanation and justification, and agency – in sum, develop mathematical power.
 Develop knowledge of children’s mathematical thinking – how children think about mathematics and how they learn it.
 Learn how to recognize and create good problems and worthwhile tasks that engage students, build on students’ thinking and experiences, leverage their home and community knowledge, and address important mathematics.
 Develop teaching practices of eliciting, interpreting, and responding to students’ mathematical thinking.
 Learn how to establish a classroom environment that promotes equitable participation and provides opportunities for all students to work at a level of productive mathematical challenge.
 Develop teaching practices involved in conducting discussions of students’ mathematical thinking.
 Develop new tools to support the teaching and learning of mathematics.
Course Outline
Teaching:
 Overview of the course, assignments, flow of class, and expectations
 What is mathematics?
 What do we believe about how children learn mathematics?
 Setting norms for our professional and mathematical work together
Looking Ahead
 Introduce “Math Autobiography” assignment
Teaching:
 Choosing good problems (Jacobs & Ambrose 2008; Jacobs & Phillip, 2010; Van de Walle, et al., 2012)
 Maintaining the cognitive demand (Stein, Smith, Henningsen, & Silver, 2000) of a problem (link to Task Analysis guide)
Due:
 Math Autobiography
Teaching:
 Eliciting and responding to children’s thinking
Looking Ahead:
 Introduce “Math Case Study” [3 ProblemSolving Interviews]
 Hand out “Getting to Know You” interview.
Due:
 Select casestudy student
Teaching:
 Instructional Activity: Counting collections (link)
Design Plans:
 Introduce “Making for Learning” project; Coffee cup tutorial in Tinkercad (at “tinker/dabble“)
Looking Ahead:
 Math Case Study: Discuss “Getting to Know You” interviews. Hand out ProblemSolving Interviews
Due:
 Write Up for “Getting to Know You” Interview for Math Case Study
Teaching:
 Eliciting and responding to children’s thinking
 Instructional Activity: True/False Equations (link)
Design Plans:
 Intro ticket: What design are you thinking about?
 Assign: Design Idea assignment
Looking Ahead:
 “Math Case Study”: Discuss Addition and Subtraction Interview results.
 Discuss Multiplication and Division problems.
Due:
 Problem Solving Interview #1
Teaching:
 Instructional activity: Choral Counting (link)
 The power of manipulatives
Design Plans:

Design Idea Assignment Due

Assign Project Rationale

Design Time 1 (1 hr)
Teaching:
 Positioning students competently (Complex Instruction)
 Setting and maintaining expectations for student participation
Design Plans:

Design Time 2 (1 hr)
Teaching:
 Problem Solving Lesson
 “Math Case Study”: Go over guidelines for final writeups.
Design Plans:
Design Time 3 (1 hr)
Due:
 Project Rationale
Teaching:
 The Two Norahs: Differently Constructed Learners (link)
 Review notes on 2^{nd} PS interview
Due:
 Problem Solving Interview #2
Teaching:
 Relational and operational thinking
 The big ideas of algebra
 Instructional Activity: Number Strings (link)
Design Plans:
 Inclass time to work on project interview tasks
Due:
 Final Write Up for “Math Case Study”
Teaching:
 Adapting a textbook lesson to engage all learners in problem solving
Design Plans:
 1hr checkin about “Making for Learning” project. Submit interview tasks by the end of class.
Teaching:
 The development of geometric thinking
 Attributes and properties of shape
Teaching:
 Mathematics as a powerful and relevant tool for understanding and influencing realworld phenomena
Teaching:
 Project Presentations