Identify Key Background Knowledge in Math Problems¶

Strategy · All strategies
Evidence · 2 claims (2 for) · 5 studies (3 causal, 2 quant-synthesis), q3–q4 · 2 of 5 report an effect size

Description¶

Before teaching a math problem, the teacher systematically identifies the background knowledge — vocabulary, cultural references, real-world contexts, and prerequisite concepts — that learners need to comprehend the problem statement itself, separate from the target mathematics. The teacher brainstorms the questions learners might ask (both relevant and irrelevant), then plans how to supply the missing knowledge. This area is especially powerful for collaboration between math teachers and ELL/ESL specialists.

Design Implications¶

Math word problems are reading comprehension tasks before they are mathematics tasks; comprehension of the surface story depends heavily on prior knowledge, and learners lacking that knowledge fail on problems they could otherwise solve Comprehension of text depends on relevant prior knowledge. [+S]. Language complexity in problem statements independently depresses performance for English learners even when the mathematics is unchanged Language complexity of math items reduces ELL performance independent of math difficulty. [+S]. Identifying the needed knowledge in advance lets teachers activate it explicitly rather than leaving learners to fail on comprehension, not math.

Context¶

Requirements¶

• A worked analysis of each problem: list every term, context, and cultural reference a learner might not know (e.g., a problem about a coupon and sales tax at a dog groomer requires knowing dog groomer, sales tax, coupon, deluxe, estimate, discount)
• Collaborative planning time between math teachers and ELL specialists to anticipate learner questions
• A plan for supplying the knowledge: pre-teaching vocabulary, Analogies to familiar contexts, or Advance Organizers

Constraints¶

• Requires planning time and cross-disciplinary collaboration that many schedules do not support [-W]
• Over-scaffolding every unfamiliar term can strip problems of the contextual reasoning they are meant to develop [~M]; the goal is comprehension of the problem, not elimination of all challenge
• Pre-teaching vocabulary in isolation, without connecting it to the problem context, produces weaker gains than integrated activation [~M]

Implementation Variability¶

• Teacher-side analysis only (anticipating questions when planning) vs. learner-side activity (students brainstorm their own questions about a problem, which doubles as comprehension monitoring)
• Whole-class pre-teaching vs. targeted support for identified ELL subgroups
• Rewriting or simplifying problem language (e.g., as in modified math assessments) vs. keeping language intact and building knowledge instead

Target Learners¶

• English language learners in mainstream math classrooms, who face a double burden of language and mathematics Language complexity of math items reduces ELL performance independent of math difficulty. [+S]
• Learners from cultural backgrounds unfamiliar with the problem's context (e.g., sales tax conventions, sporting rules)
• Struggling readers whose decoding load competes with mathematical reasoning for working memory Extraneous load from comprehension demands degrades problem-solving performance. [+S]

Target Learning Goals¶

• Problem comprehension: understanding what a word problem is asking before solving it
• Vocabulary and discourse of mathematics (terms like percent off, regularly priced, estimate)
• Transfer of reading-comprehension strategies to mathematical contexts

Instructions¶

1. Select the problem and solve it yourself, noting every step.
2. List all terms, contexts, and cultural references in the problem statement; brainstorm the questions learners might ask, including irrelevant ones.
3. Sort the list: what is essential to the mathematics, what is incidental, what can be learned from context.
4. Plan activation: pre-teach essential vocabulary, use Analogies to familiar contexts, or have students generate and discuss their own questions about the problem.
5. Teach the problem, monitoring comprehension of the scenario separately from the mathematics.

Related Strategies¶

• Activating Prior Knowledge — the general strategy this applies to math word problems
• Accessible Syntax — complementary language-side support for math problem text

Examples¶

• A problem about a fishing pole on sale: before solving, the class discusses What is "percent off"? What is a sale? What does "regularly priced" mean? — then solves.
• A problem set on sales tax at a dog groomer: the ELL specialist pre-teaches coupon, discount, and deluxe with images; the math teacher connects them to the percent operations in the problem.
• Modified assessment items (as studied by Abedi & Lord) that shorten and simplify problem language show the same principle from the item-design side.

Key Sources¶

• Abedi, J., & Lord, C. (2001). The language factor in mathematics tests. Applied Measurement in Education, 14(3), 219–234. doi:10.1207/s15324818ame1403_2
• Recht, D. R., & Leslie, L. (1988). Effect of prior knowledge on good and poor readers' memory of text. Journal of Educational Psychology, 80(1), 16–20. doi:10.1037/0022-0663.80.1.16
• Cummins, J. (1984). Bilingualism and special education: Issues in assessment and pedagogy. Clevedon: Multilingual Matters.
• Sweller, J., Ayres, P., & Kalyuga, S. (2011). Cognitive load theory. Springer. doi:10.1007/978-1-4419-8126-4