The Elementary Mathematics Project (EMP) is an NSF-funded project out of Boston University whose overarching goal is to develop and disseminate learning materials that strengthen pre-service elementary teachers’ understanding of mathematics. Learn More.

Improving Pre-Service Elementary Teachers’ Mathematical Knowledge for Teaching

Our Mission

Mathematical knowledge for teaching (MKT) refers to the “mathematical knowledge needed to carry out the work of teaching mathematics” (Ball, Thames, & Phelps, 2008). Simply knowing how to do mathematics is not sufficient; teachers must also know the mathematics they teach deeply and in ways that can help their students learn. The importance of developing this mathematical knowledge through coursework and professional development is undeniable (CBMS, 2012).

In light of this need, our mission is two-fold: 1) to develop and test learning materials to improve pre-service elementary teachers’ mathematical knowledge for teaching; and 2) to develop and test instructor support materials to grow faculty expertise in using our learning materials in their content and methods courses.

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Development of EMP Learning Materials

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The primary teaching strategy built into the EMP learning materials is the focused use of discussions and argumentation

50+ Lessons and Support Materials

The EMP curriculum includes more than 50 lessons and corresponding support materials spanning 7 key mathematical content areas, or units. These units can be combined in different ways to create two or three college-level courses (depending on credit hours) for teaching mathematics content to future elementary teachers.  The content and pedagogies used in the EMP instructional materials align with recommendations from the Association of Mathematics Teacher Educators’ Standards for Preparing Teachers of Mathematics and the Conference Board of the Mathematical Sciences’ Mathematical Education of Teachers I and II reports. Content focuses on essential concepts and procedures that future elementary teachers need to understand. The lessons were designed to be taught using inquiry and research-based instructional strategies. For example, in order to support the construction of shared meaning, PTs participate in discourse communities where learning revolves around discussions, student-led presentations, and problem solving.

The EMP curriculum includes support materials (print, interactive software, and videos) for faculty members. The support materials include general information related to all units such as documents about setting classroom norms and using discussion-based instruction; information related to each specific unit such as documents about online teaching and the key mathematical ideas; and information related to each specific lesson such as Instructor’s Guides and homework files.  These materials are educative – namely, they were designed so that faculty members could learn from them. Educative features of the Instructor’s Guides include: a) elaborations of the mathematical content, including representations regularly used in elementary instruction, b) suggestions for how to use student-centered pedagogies, c) information about the instructor’s role as a co-participant in the community, d) details about PTs as learners of this content, and e) connections to teaching elementary children the content.

Key Mathematical Content Areas

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    The Fractions unit consists of 10 mathematical lessons that explore important fraction concepts as well as fraction operations. Topics studied include the concept of a fraction, equivalent fractions, fraction comparisons, addition and subtraction of fractions, multiplication and division of fractions, and converting fractions to decimals.  These lessons emphasize topics that are most relevant to the teaching of children in grades K-5, and are mentioned in the Common Core State Standards for Mathematics (2010).

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    Number Theory

    The Number Theory unit consists of 6 mathematical lessons that explore important number theory concepts and procedures typically studied starting in the elementary grades. Topics studied include factors, prime factorization, divisibility, divisibility rules, greatest common factor, and least common multiple. Emphasis is placed on developing a deeper understanding of the multiplicative structure of integers, a central concept in number theory that supports other critical topics in the elementary grades.

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    Geometric Measurement

    The Geometric Measurement unit consists of 9 mathematical lessons that explore foundational measurement concepts as well as the justifications of key measurement formulas. Topics studied include area concepts, area and perimeter relationships, area formulas, surface area, and volume. In the Mathematical Education of Teachers II (Conference Board of Mathematical Sciences, 2012) document, these topics are mentioned as ones that future teachers of elementary school students should have opportunities to study in depth.

    NOTE: See the Geometry unit for an alternate, updated version of the Prisms lesson that can be used instead of the version posted here.

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    The Geometry unit consists of 11 mathematical lessons that explore core concepts in two-dimensional Euclidean geometry as well as solid geometry. Topics studied include sorting attributes, defining angle, parallel and intersecting lines, defining polygons, classifying and constructing triangles, classifying quadrilaterals, the sum of interior angles of polygons, tessellations, visualization with nets, and prisms. A running theme throughout the unit is on classifying shapes by their attributes.

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    Number Concepts

    The Number Concepts unit consists of 6 mathematical lessons that explore important concepts related to the place value number system. Topics studied include characteristics of the base-ten place value system, different place values, large numbers, decimals, modeling decimal quantities, comparing and ordering decimal quantities, and representing fractions as decimals. There is an extensive focus on place value structure and modeling throughout the unit.

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    Addition & Subtraction

    The Addition & Subtraction unit consists of 7 mathematical lessons focused on the addition and subtraction operations. Topics studied include addition and subtraction story problems, addition strategies and algorithms, subtraction strategies and algorithms, and addition and subtraction of decimals. There is significant attention placed on number decomposition, number line modeling, and the arithmetic properties throughout the unit.

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    Multiplication & Division

    The Multiplication & Division unit consists of 8 mathematical lessons focused on the multiplication and division operations. Topics studied include multiplication and division situations, multiplication strategies and algorithms, multiplication games, measurement and partitive division, division strategies and algorithms, and multiplication and division of decimals. Across lessons, there is an emphasis on array models and on the distributive property.

Written Lesson Materials

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Become an EMP User

Our written and multimedia materials are currently available for general dissemination. If you are interested in using our written and/or multimedia materials in a mathematics content or mathematics methods course, please contact Suzanne Chapin at or

Multimedia Materials

Video clips to support faculty members in using more student-centered instruction are used by this project. There are 192 video clips across the EMP lessons (1 to 5 videos per lesson). Furthermore, another 108 video clips are in the searchable EMP Video Library.  The video library is organized around five categories: DiscourseMathematical ReasoningNorms, Pedagogical Challenges, and Extended Clips. The videos provide images of experienced instructors teaching future elementary teachers in mathematics content courses. Each video includes preservice teachers grappling with complex ideas from an EMP lesson and instructors facilitating participants’ engagement with the content. Commentary from the curriculum designers accompanies each clip to provide context, highlight particular actions and questions made by the instructors or students, or explain the instructor’s decision-making.

The EMP project team also created supports for synchronous online teaching of the EMP lessons.  Information for using EMP online outlines strategies, tools, and resources for establishing community and norms, setting up routines for small group work, structures for increasing engagement, and ideas for using online tools such as Google Slides and Jamboards. Additionally, for all 57 lessons, online lesson guides suggest which problems are best to have students work on prior to a class meeting, during small group time, and during whole group time.  These lesson-specific guides contain Google Slide presentations that can be edited collaboratively by faculty and students.  There are also tips for engaging students, collecting feedback, and using the chat and video features during online class time.