Are your students Writing About Mathematics? Or, are they Engaged in Mathematical Writing?
Teachers have received limited guidance about writing during math instruction (Casa, Evans, Firmender, & Colonnese, 2017). Because of this, it is important to distinguish between writing about mathematics and mathematical writing. Writing about mathematics prioritizes the learning of literacy; but mathematical writing emphasizes mathematical reasoning (Casa, et al., 2017). This type of writing includes text, but also symbols, numerals, operations, pictures, charts, tables (Casa, et al., 2017). The overarching goal for mathematical writing is for students to reason mathematically and communicate ideas (Casa, Cahill, Cardetti, Choppin, & Cohen, 2016). Writing helps students justify and explain their ideas in order to make their reasoning clear (Casa, et al., 2016).
How can you incorporate mathematical writing into lessons?
First, consider the specific purposes of each type of mathematical writing:
- Exploratory: To personally make sense of a problem or one’s own ideas
- Informative: To describe or explain thoughts (“Explain your strategy, “What do you notice”…)
- Argumentative: To construct or critique an argument (“How do you know?”, “Convince a classmate”, “Do you agree or disagree and why?”….)
- Mathematically Creative: To elaborate ideas, document original ideas, or extend thinking beyond the original problem
Next, select prompts that encourage students to produce the type of mathematical writing that you desire. This ensures that the writing has the greatest possible impact on students’ math learning (Firmender, Casa, & Colonnese, 2017).
Finally, provide sentence starters to help students begin to write such as, “I agree with ____ because___”. This helps students organize their thinking and provides them with a starting point for writing.
Mathematical writing is a tool that can be used to further students’ reasoning and communication in all grade levels, starting in kindergarten; and it applies to all types of learners, including students with disabilities, English language learners, and students identified as gifted. (Firmender, Casa, & Colonnese, 2017).
Casa, T., Cahill, J., Cardetti, F., Choppin, J., & Cohen, J. (2016). Types of and purposes for elementary mathematical writing: Task force recommendations. Retrieved from http://mathwriting.education.uconn.edu
Casa, T., Evans, K., Firmender, J., & Colonnese, M. (2017, February). Why should students write in math class? Educational Leadership, 74(5).
Firmender, J., Casa, T., & Colonnese, M. (2017). Write on: Promote students’ reasoning with different types and purposes for mathematical writing. Teaching Children Mathematics, 24(2), 85-92.
Enhanced Scope and Sequence
The SOL Enhanced Scope and Sequence (ESS) was created by a team of general and special educators and VDOE personnel. ESS provides teachers across the state with differentiated lessons that are aligned with the essential knowledge and skills found in the Curriculum Framework at VDOE. The ESS is organized by content areas (i.e. Mathematics, English, History and Social Science, Science), and can be accessed at the Virginia Department of Education Standards of Learning.
Virginia Department of Education Instructional Resources
- The Standards and SOL-based Instructional Resources
- Math ESS Lessons
- English ESS Lessons
- Science and Social Studies ESS Lessons
Suggestions for Communicating With and About People with Disabilities at the CDC.
Virginia Department of Education Mathematics Resources
- Tests and Sample Item Sets Released in Spring 2014 (Grade 3, Grade 4, and Grade 5)
- VDOE Mathematics Resources
- Algebra Readiness Inventory Curriculum Companion
- Web Tour of the ARI Curriculum Companion
- Mathematics Word Wall Cards
- VDOE Guidelines for Educating Students with Specific Learning Disabilities in Math
T-TAC Online Math Resources
Additional Mathematics Sites of Interest
Fluency Without Fear by Jo Boaler (activities to develop Number Sense and Number Facts)
Watch this NCETM video of a teacher using multiple representations for multiplication. (This teacher works in a school where 3 x 4 is interpreted as 3 + 3 + 3 + 3). It is a good example of how to support the conceptual understanding of multiplication facts and its importance as students develop fact fluency.
Quantiles Framework Resources
- Quantiles Teacher Assistant and Quantiles Math Skills Database Search
- Web Tour of the Quantiles Framework Tools
Newly Added Resources
At the National Center on Intensive Instruction website, you can find examples of instructional plans that intensify fraction instruction. You can download the plans and print-based representations (manipulatives) at the links below.