Math Key Word Flashcards¶

Strategy · All strategies
Evidence · 3 claims (3 for) · 12 studies (5 quant-synthesis, 4 causal, 2 review, 1 associational), q2–q4 · 3 of 12 report an effect size

Description¶

Learners create flashcards for each of the four mathematical operations. On one side, they write the operation and symbol (+, −, ×, ÷); on the other, they list key words associated with that operation (e.g., "sum," "altogether" → addition; "how many more" → subtraction). Students use the flashcards as visual aids during word-problem practice and math coaching, adding new key words as they encounter them.

Design Implications¶

Generating the cards is itself a form of elaborative encoding — learners must retrieve, organize, and articulate associations, which supports retention better than reading a pre-made list Self-explanation improves conceptual understanding. [+M]. Grouping key words by operation chunks the vocabulary into a small, retrievable set, reducing working-memory load during problem solving Chunking reduces working memory load. [+M]. However, the key-word strategy is a heuristic, not a comprehension strategy: it works only when surface language reliably signals the operation, so it should be paired with instruction in problem structure (situations, quantities, relationships) rather than replacing it.

Context¶

Requirements¶

• Index cards, markers or colored pencils
• A curated set of authentic word problems for practice, so key words are encountered in context
• Direct instruction on each operation's meaning before key words are mapped to it

Constraints¶

• Key words are unreliable cues: "left" can indicate subtraction or comparison, "of" signals multiplication in one context and division in another, and multi-step problems routinely contain key words pointing to the wrong operation [~M] — learners trained to translate words directly to operations perform worse on non-routine and multi-step problems [-M]
• Rote card drilling without word-problem practice produces vocabulary recall that does not transfer to solution accuracy [-M]
• Time-consuming to create; pre-made cards sacrifice the generative encoding benefit [+W]
• Less effective for learners who already read flexibly for problem structure, for whom the cards add redundancy [~W]

Implementation Variability¶

• Learner-generated vs. teacher-provided cards (generation is preferable for encoding)
• Physical cards vs. digital decks (e.g., Quizlet) with spaced review Spaced repetition improves retention. [+S]
• Cards extended to include non-examples — key words that are not reliable cues — to build discrimination
• Cards used as a sorting activity (sort word problems by operation) rather than a lookup aid

Target Learners¶

• Students in grades 3–8 still building fluency connecting everyday language to mathematical operations [+W]
• English language learners, for whom the cards serve as an accessible-vocabulary scaffold Accessible vocabulary and syntax supports comprehension. [+M]
• Struggling readers who benefit from a concrete external reference during problem solving [~M]

Target Learning Goals¶

• Vocabulary–symbol associations for the four operations
• Initial word-problem orientation: identifying which operation a situation calls for
• Not appropriate as a terminal goal: comprehension of problem structure and multi-step reasoning require going beyond key words [-M]

Instructions¶

1. Introduce each operation's meaning with Direct Instruction, using concrete situations before naming key words.
2. Learners create one card per operation, writing the symbol on the front and brainstorming key words for the back; supplement with words harvested from a shared set of word problems.
3. Sort or verify: present sample word problems and have learners use their cards to propose an operation, then check by modeling the situation (Practice).
4. During coaching or homework, learners keep cards available as a visual aid and add newly discovered key words, flagging any word that pointed to the wrong operation.
5. Fade the cards as learners shift attention to problem structure — quantities, relationships, and questions asked — rather than isolated vocabulary.

Related Strategies¶

• Cognitively Guided Instruction — the structural alternative: key words are subordinated to understanding problem situations
• Analogies — mapping new key words to known situations deepens the association
• Spaced retrieval practice [+S] — schedule card review for durable vocabulary retention

Examples¶

• A grade 4 class creates addition/subtraction cards, then sorts a deck of one-step word problems into operation piles, discussing the "how many more" cases where the cue is ambiguous.
• An ELL support block uses bilingual cards (English word, home-language translation, symbol) during small-group problem solving.
• Quizlet decks ("Multiplication key words") used for brief spaced warm-ups before word-problem practice.

Key Sources¶

• Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Swets & Zeitlinger.
• Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18–32. doi:10.1037/0022-0663.87.1.18
• Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Loef, M. (1989). Using knowledge of children's mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531. doi:10.3102/00028312026004499
• Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). Improving students' learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4–58. doi:10.1177/1529100612453266