Students should be exposed to the same vocabulary year after year. The name of a strategy shouldn’t change from one grade to the next as this causes confusion.
Vocabulary and strategy names should be mathematical in nature. For example, “The turtle strategy for two digit by two digit multiplication” has students follow these steps: Draw the turtle’s head. Multiply by the number in its neck. Check off carried numbers. Draw a collar and lay a turtle egg (zero). Multiply by the other number. We don’t “lay eggs” when multiplying. Putting a collar on the turtle is not mathematical. This “strategy” can’t be transfered beyond two digit by two digit multiplication. They aren’t solving the question with any mathematical understanding of how multiplication works nor applying their understanding of place value.
Alberta Education has provided a document containing and explaining Directing Words for Mathematics. Although this document was prepared for Grade 12 students as a support for Diploma Exams, the directing words and their explanations can be used at earlier grade levels. By utilizing them in earlier grades, teachers can build consistent language use with their students.
Rocky View School Division created a list of vocabulary words by grade using the Alberta K-9 Math Program of Studies (including Achievement indicators).
Caution: Teaching “Key Words”
When students are working with word problems, they are often introduced the acronym “C.U.B.E.S.” or another acronym that essentially follows the same format:
- Circle all key numbers.
- Underline the question.
- Box any key words.
- Eliminate unnecessary information.
- Solve and check.
These same students are often taught that “in total” or “more” means you will add and “less” means you will subtract. Consider the following question: Your garden has 3 rows of carrots. There are 15 carrots in each row. How many carrots are there in total?
The phrase “in total” can be used for all four operations, not just addition. This blog post explores the reasoning for avoiding teaching students that a key word has a specific operation attached to it and provides an idea for teaching students to understand the word problem.
Alberta Education’s Directing Words for Mathematics for Math 30-1 and 30-2.
Alberta Regional Professional Development Consortia developed the Elementary Professional Learning site. They have included vocabulary documents for:
- Equality: Equality, Attribute, Conservation of number, Mathematical Reasoning, Mathematical Connections, Mathematical Problem Solving, Symbolically, Concretely, Pictorially, Equation, Variable, Preservation of Equality
- Additive Thinking: Addend, Associative Property, Commutative Property, Compensation, Constant Difference, Decomposing Numbers, Difference, Friendly Numbers, Inverse Operation, Minuend, Partitioning, Subtrahend, Sum
- Multiplicative Thinking: Area Model / Rectangular Array, Associative Property, Cartesian Product, Commutative Property, Composite Number Distributive Property / Partitioning, Factor, Greatest Common Divisor/Factor, Inverse Operation, Iteration, Least/Lowest Common Multiple, Multiple, Multiplicative Comparison, Multiplicand, Multiplier, Product, Dividend, Divisor, Quotient, Rate, Ratio, Prime Number
- Assessment: Criteria for Success, Evaluation, Feedback, Formative assessment (assessment for learning), Including, Learning intention, Learning outcomes, Peer Feedback, Self-evaluation/self-assessment, such as, Summative assessment (assessment of learning)
- Instructional Practices: Additional Support Resources, Algorithm, Approved Resource, Authorized Resource, Classroom Culture, Conceptual Understanding, Concrete Stage, Constructivism, Critical Thinking, Differentiated Instruction, Direct Instruction, Discourse, Discover Learning, Effective Strategy, Efficient Strategy, Fixed Mindset, Flipped Classroom, General Outcomes, Growth Mindset, Inclusion, Inquiry-based Learning, Instruction, Instructional Practices, Instructional Strategies, Manipulatives, Mathematical Processes, Mathematical Strategies, Outcome, Pictorial Stage, Programming Principles, Resource, Responsive Instruction, Required Resource, Specific Outcome, Symbolic Stage, Virtual Manipulatives
Math is Fun – Illustrated Mathematics Dictionary – Mathematics Vocabulary & Illustrations
Mathematics Glossary – LearnAlberta.ca
- Example Link – Associative Property
Rocky View School Divisions: Vocabulary by Grade