Supplementary Materials for AMTE Standards
The Standards for Preparing Teachers of Mathematics elaborate what beginning teachers of mathematics must know and be able to do as well as the dispositions they must have to increase equity, access, and opportunities for the mathematical success of each of their future students. The following set of resource materials are intended to support mathematics teacher educators in developing mathematics teacher candidates’ knowledge and skills for selecting, planning, and enacting a variety of technology to support and facilitate effective mathematics teaching.
Documents for Mathematics Teacher Educators
- Technology Plan Template. Planning template that accompanies a mathematics lesson plan and focuses teacher candidates’ attention on choosing technology uses to enhance one or more specific mathematics teaching practices. The template is accompanied by a reflection on planning for and teaching with technology.
- Framework for Evaluating Digital Instructional Materials (DIM) – Student Handout. Teacher-generated framework for evaluating digital instructional materials and integrating technology to enhance effective mathematics teaching practices. The dimensions of the framework are grounded in research in mathematics education and technology integration in teaching, whereas the specific indicators and examples were provided by practicing K-8 teachers of mathematics.
- Implementation Guide for Using the DIM Framework. The implementation guide includes a description and context for using the DIM framework (the framework for evaluating digital instructional materials), descriptions of learning activities, and discussion prompts.
- Lesson Reflection. General reflection on possible technology integration for a mathematics lesson plan that teacher candidates write in a methods course and enact in a practicum setting. Reflection prompts provide an opportunity for teacher educators to assess teacher candidates’ growth in selecting, planning, and enacting a variety of technology to support and facilitate effective mathematics teaching.
- Accompanying Examples of Teacher Candidate Work. Blinded samples of lesson reflections, technology plans, and technology planning reflections by beginning elementary teachers of mathematics. Examples show a range of responses and illustrate potential growth throughout a series of lesson plans.
- Reflections includes prospective teachers’ responses to prompts in Lesson Plans 1 and 3. Lesson Plan (LP) 1 reflections tended to focus on add-on or skills practice and ways for prospective teachers to convey information to students. Lesson Plan (LP) 3 reflections tended to focus on using technology to engage students in mathematical discourse and connecting among mathematical representations.
- LP2 Grade 1 Sample In this sample, the candidate describes a technology the teacher could have used to elicit and use student understanding. The Plickers app would be used as a formative assessment, which the candidate identifies as a replacement for what was done in the technology without technology.
- LP2 Grade 3 Sample In this sample, the candidate suggests using virtual base ten blocks to use and connect mathematical representations. The candidate identifies this technology use as amplification or transformation. While virtual manipulatives could be used as a replacement for physical manipulatives, this candidate did not use any manipulatives during the lesson, so the use of virtual manipulatives would have been more than a replacement.
- LP3 Grade K Sample This candidate identified the use of iTools: Addition and Subtraction (a suite of virtual manipulatives) as a way to amplify building procedural fluency from conceptual understanding and using and connecting mathematical representations. In this case, the candidate planned to use the iTools to convey multiple representations of Kindergartners’ story problems. Although students would not interact directly with the technology, the candidate plans to use the technology for a specific teaching purpose related to effective mathematics teaching practices.
- LP3 Grade 3 Sample In this example, the candidate plans to use an iPad camera and AirPlay to amplify how she facilitates mathematical discourse during the lesson. While the technology is not mathematics-specific, the candidate focuses on students’ use of the iPad for sharing and explaining their work. She highlights how the technology would enable students to do so more effectively than tools normally used in her classroom.
Standards and Indicators these Materials Target
The compiled set of resource materials are aligned with AMTE Standards for Preparing Teachers of Mathematics Indicators C.1.6, C.2.2, and C.2.3 as detailed below.
- C.1.6. Use Mathematical Tools and Technology. Lesson Reflection, Technology Plan, “Well-prepared beginners recognize the fast rate at which technologies emerge and are committed to staying abreast of new tools, analyzing their potential and limitations for students’ mathematics learning.” (p. 12)
- C.2.2. Plan for Effective Instruction. Technology Plan, “Therefore, well-prepared beginners strive to design classroom environments in which students have opportunities to communicate their thinking, listen to the thinking of others, connect mathematics to a variety of contexts, and make connections across mathematical ideas and subject areas.” (p. 14)
- C.2.3. Implement Effective Instruction. Lesson Reflection, Technology Plan, Technology Reflection,
“Teachers must not only understand the mathematics they are expected to teach (Ball, Thames, & Phelps, 2008) and understand how students learn that mathematics (Fuson, Kalchman, & Bransford, 2005), they must be skilled in using content-focused instructional pedagogies to advance the mathematics learning of each and every student (Forzani, 2014).” (p. 15)
Notes on Implementation
The compiled set of resources are intended for teacher methods courses that occur early in teacher candidates’ preparation program. The resources are designed flexibly for mathematics teacher educators to support existing lesson planning, teaching, and reflecting work where teacher candidates want to use technology to enhance teaching and learning of any mathematics content. The term “digital instructional materials” is used to broadly encompass digital curriculum materials, mathematical tools, communication tools, or any other digital technologies that teachers might implement in a classroom for the purposes of teaching and learning mathematics. (For a more complete description of how teachers defined “Digital Instructional Materials” see Thomas & Edson, 2018). A broad definition of technology recognizes the vast differences among candidates’ access to and facility with tools and devices, thus “meeting them where they are” with respect to technology knowledge and access. Teacher educators who wish to focus on particular technologies (e,g., mathematics-specific tools) might elect to omit or limit the use of some materials included here.
A key assumption with the developed resources is that mathematics teacher educators engage teacher candidates with planning, teaching, and reflecting on mathematics lessons. The set of materials is intended to be used throughout the duration of the course and is NOT considered a set of resources to comprise any single class session. The compiled set of resources can be embedded within the evaluation work that mathematics teacher educators might typically do with lesson plans and technology. Thus, the materials are designed to strengthen technology components in mathematics lessons without creating additional evaluation work.
The developed materials are designed for implementation in an elementary, middle grades, or secondary mathematics methods course and associated practicum. The materials have been previously implemented and revised in courses with approximately 25 beginning elementary teachers of mathematics. In these particular courses, teacher candidates plan, teach, and reflect on three mathematics lessons throughout the semester. The use of technology was optional for planning and teaching components of Lesson Plans 1 and 2, as these were the first mathematics lessons most of the students had ever taught.
In the particular course where these materials were developed, candidates first focus on learning to plan for and implement effective and equitable mathematics teaching practices as described in Principles to Actions (NCTM, 2014), while simultaneously using technology as learners in the methods course and observing technology use in the practicum setting. By Lesson Plan 3, candidates are expected to incorporate technology in their own planning and teaching of mathematics lessons for students. Although a practicum experience was linked to our course, the materials could be adapted for use in a variety of lesson planning contexts.
The following table summarizes the three lesson implementation cycles that span across a course: Planning – Teaching – Reflecting, and how the compiled set of resources overlay with the lesson plan implementation cycles. The compiled set of resources also includes accompanying examples of work by mathematics teacher candidates.
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Lesson Plan 1 |
Lesson Plan 2 |
Lesson Plan 3 |
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Planning |
Optional Use of Technology |
Optional Use of Technology |
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Teaching |
Optional Use of Technology |
Optional Use of Technology |
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Reflecting |
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Mathematics teacher educators or teacher candidates can read more about the DIM Framework and teachers’ definitions of DIMs in the references below.
Thomas, A. & Edson, A.J. (2017). A Framework for Mathematics Teachers' Evaluation of Digital Instructional Materials: Integrating Mathematics Teaching Practices with Technology Use in K-8 Classrooms. In P. Resta & S. Smith (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference 2017 (pp. 11-18). Chesapeake, VA: Association for the Advancement of Computing in Education (AACE).
Thomas, A. & Edson, A.J. (2018). An examination of teacher-generated definitions of digital instructional materials in mathematics. In L. Trouche, G. Gueudet, & B. Pepin (Eds.) Proceedings of Re(s)sources 2018 conference: Understanding teachers’ work through their interactions with resources for teaching. Lyon, France.
About the Authors
- Alden J. Edson, Michigan State University
- Amanda Thomas, University of Nebraska-Lincoln