Learn About Students' Math Backgrounds¶

Strategy · All strategies
Evidence · 2 claims (1 for, 1 mixed) · 3 studies (2 review, 1 associational), q2–q3 · 1 of 3 report an effect size · 1 claim rests on one study

Description¶

This strategy involves deliberately eliciting what learners already know and can do mathematically — formal schooling history, informal and practical skills (sports statistics, family finances, measurement systems used at home), and interests — before and during instruction. Teachers then connect new content to that knowledge, group learners intentionally, and create leadership opportunities so learners can demonstrate competence in multiple ways. It is foundational for adult basic education, multilingual classrooms, and any setting where prior schooling varies widely.

Design Implications¶

Prior knowledge is one of the strongest predictors of how much a learner takes from instruction, and interest interacts with it: learners with low prior knowledge benefit from situational interest, while high-knowledge learners benefit more from individual interest Interest and prior knowledge jointly shape learning outcomes. [~M]. Teachers who use detailed knowledge of children's informal mathematical thinking to guide instruction produce substantially larger learning gains than those following the textbook alone [+S]. Knowing backgrounds also lets teachers avoid activating misconceptions or culturally unfamiliar contexts that add extraneous load.

Context¶

Requirements¶

• Diagnostic activities that surface both formal skills and informal strategies (interviews, open tasks, Check-Ins)
• Willingness to treat home and community mathematics as legitimate resources, not deficits
• A mechanism for feeding what is learned into planning — task contexts, examples, grouping decisions
• Sensitivity to learners' numeric and measurement systems, especially for English language learners

Constraints¶

• Gathering individual background information takes sustained time; superficial surveys yield stereotypes rather than usable knowledge
• Assumed "gaps" can be wrong — learners with limited formal schooling often have strong informal reasoning, and treating them as empty vessels depresses expectations [-M]
• Prior knowledge that is incomplete or misconceived can interfere with new learning if activated without correction [~S]
• Grouping by "background" risks tracking and stigma; grouping must be task- and sensitivity-driven [-M]

Implementation Variability¶

• One-time diagnostics at course start vs. ongoing elicitation embedded in each unit
• Home-visit and community-based approaches (common in adult literacy and early-childhood programs) vs. classroom-only methods
• Learner self-report (interest inventories, math autobiographies) vs. performance-based diagnostic tasks

Target Learners¶

• Adult basic education and English language learners with highly variable schooling histories [+M]
• Learners whose informal math competence exceeds their formal register — leadership and teaching roles let them demonstrate and consolidate knowledge Self-efficacy built through successful performance supports persistence. [+M]
• All learners benefit, but the payoff is largest where classroom assumptions about "typical" preparation are most likely to be wrong

Target Learning Goals¶

• Conceptual connections: linking new procedures to learners' existing informal strategies
• Transfer: applying math to personally meaningful contexts (budgeting, sports, work)
• Equity of participation: ensuring learners with non-dominant schooling backgrounds can engage and lead

Instructions¶

1. Elicit prior knowledge with open diagnostic tasks and interviews rather than only placement tests — use Activation and Check-Ins to surface informal strategies and misconceptions
2. Document what learners know about contexts, currencies, and measurement systems they actually use; note interests and responsibilities
3. Design tasks anchored in those contexts, using Analogies to bridge informal and formal representations
4. Group intentionally and with sensitivity — mixed-background groups where stronger informal reasoners can lead, with rotating Application roles so every learner demonstrates competence publicly
5. Revisit and update background knowledge continuously; treat it as formative information, not a fixed label

Related Strategies¶

• Activating Prior Knowledge — the in-lesson counterpart: this strategy supplies the knowledge base that activation draws on
• Accessing Students' Background Knowledge — broader content-area version of the same diagnostic work
• Activate Background Knowledge — lesson-level routines for surfacing what learners bring
• Use ongoing assessments to tailor early-childhood learning experiences

Examples¶

• Cognitively Guided Instruction (CGI for Math) — teachers learn research-based maps of children's informal addition/subtraction strategies and use interviews with their own students to plan instruction; a well-documented model of background knowledge driving teaching decisions
• Adult basic education intake interviews — programs such as community-college developmental math redesigns use math autobiographies and informal assessment conversations to place learners by strategy use, not just test scores
• Home- and community-based context mapping — teachers visiting learners' neighborhoods (markets, workplaces, sports settings) to identify familiar quantities, prices, and measurement units for word problems

Key Sources¶

• 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
• Tobias, S. (1994). Interest, prior knowledge, and learning. Review of Educational Research, 64(1), 37. doi:10.2307/1170745
• Moschkovich, J. N. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2–3), 189–212. doi:10.1207/S15327833MTL04023_5
• Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics education for young children: What it is and how to promote it. Social Policy Report, 22(1), 3–22.