Preparing Teachers of Addition and Subtraction

Supplementary Materials for AMTE Standards

We appreciate the opportunity to develop materials related to the AMTE Candidate Standards and Indicators. These materials focus on structures of addition and subtraction for teachers of early elementary children and aligns with indicators from Candidate Standards C.1, C.2, and C.3. The set of materials will support mathematics teacher educators in developing elementary mathematics teacher candidates’ content and pedagogical knowledge relating to operations and algebraic thinking, specifically structures of addition and subtraction.

Standards and Indicators these Materials Target

The following table summarizes alignment of materials with Candidate Standards and Indicators.

  • EC.1. Deep Understanding of Mathematics: ​Operations and Algebraic Thinking (​Elaboration of C.1.1). Task 1​ requires candidates to solve addition and subtraction problems using multiple representations and, later, analyze the structures of the problems they solved. Activity A​ engages candidates in making connections between multiple representations of addition and subtraction problems and the structures those problems represent. Activity B​ presents candidates with incorrect examples and representations of specific addition and subtraction structures. Candidates will develop deeper understanding of these structures through analyzing, discussing, and correcting these errors. 
  • EC.4. Tools, Tasks, and Talk as Essential Pedagogies for Meaningful Mathematics (Elaboration of C.2.2 and C.2.3). Task 2​ ​ engages candidates in generating story problems of specific structures with unknowns in all positions. Along with this task, candidates consider contexts, attending to student funds of knowledge and interests. Task 2​ also offers candidates an opportunity to demonstrate representational competence, generate questions and prompts to support students’ problem solving, and anticipate student thinking. 
  • EC.7. Seeing  Mathematics Through Children’s Eyes (Elaboration of C.3.1). After initially solving ​Task 1​, analyzing the structures of the problems, and anticipating possible student solutions, candidates will examine a student’s solutions and video clips of explanations to these problems. Analysis of actual student work and reasoning will provide candidates an opportunity to consider the child’s understanding within a developmental progression and reveal how a child saw and solved the problems. 

About the Authors

  • Amanda Thomas, Ph.D., Assistant Professor of Mathematics Education, University of Nebraska - Lincoln
  • Michelle Homp, Ph.D., Research Professor of Mathematics, University of Nebraska - Lincoln