What is the best way to prepare your early elementary school students for algebra?
- Work on calculation skills
- Work on word problems
- Work on both word problems and calculation
- None of the above. These two skill areas have nothing to do with algebra.
The correct answer is (b), work on word problems, according to a new study in the Journal of Educational Psychology. Improved calculation skills do not transfer to algebra even when instruction is designed to help students transition to pre-algebraic thought by focusing on the equal sign, for example, write researchers Lynn S. Fuchs et al.
Nor do improved calculation skills transfer to word problems, suggesting that these 2 domains are distinct and that teachers and curriculum designers should treat them each explicitly and deliberately. The findings also suggest that screening for math difficulty requires different measures for the different domains, the authors write.
“By contrast, at the present time, research and practice focus disproportionately on calculations over word problems, perhaps with the assumption that understanding about calculation development pertains to word problems and that instruction on calculations will transfer to word problems.
“This is unfortunate given the present study’s findings and due to the importance of word problems.”
For the study, 1,917 2nd-grade students in one metropolitan school district were randomly assigned to 3 conditions: calculation intervention, word-problem intervention and control group. A total of 96 teachers (127 classes) in 25 schools participated. Both interventions included instructional linkages to pre-algebraic knowledge. One key difference between the control group and both intervention groups is that control students did not receive instruction on the equal sign as a relational term.
The calculation intervention comprised 6 units: 1. equal sign as a relational term, 2. addition concepts and operational strategies for problems for which retrieval is a viable strategy, 3. concepts for similar problems involving subtraction, 4 concepts and operational strategies for addition problems with regrouping, 5. concepts and operational strategies for subtraction problems with regrouping, and 6. review.
The word problem intervention comprised 5 units 1. foundational skills for the word-problem content (i.e., equal sign as a relational term; strategies to find x; strategies for checking word-problem work, 2. combine problems, 3. change problems 4. compare problems and 5. review.
Students were screened and assessed in September-October and research assistants delivered whole-class instruction in November-March. Tutoring was conducted from December-March. For the 2-tier calculation and word-problems interventions, assistants provided 34 whole-class intervention lessons (2 lessons per week for 17 weeks) and 39 Tier 2 lessons (3 lessons per week for 13 weeks beginning in Weeks 4-5 of Tier 1 instruction).
“Intervention improved performance in the targeted domain but not the other domain,” the researchers found. Only the word-problem intervention group showed transfer in pre-algebraic thought outcomes (Dynamic Assessment of Algebraic Knowledge, Pre-algebraic Knowledge).
Word-problem skill is the best school-age predictor of employment and wages in adulthood, according to the study. Because there are more cognitive processes involved in solving word problems than in calculations, deficits may be more complicated to prevent and remediate, the authors write.
“Does Calculation or Word-Problem Instruction Provide a Stronger Route to Prealgebraic Knowledge?,” by Lynn Fuchs et al., Journal of Educational Psychology, 2014, Volume 106, Number 4, pp. 990-1006.