Investigating mathematics content standard quality: A review of California's high-demand first-grade basic facts expectations.

摘要

Focused on accelerating mathematics achievement, California is one of only four states that has set its addition and subtraction basic facts standard for first grade students at the most demanding level along three dimensions: solve problems (a) to 20, (b) from memory, and (c) both addition and subtraction. Based on surveys of 49 teachers and assessments of 275 students from 9 diverse schools, this study examined California's standard through two lenses: (a) student achievement in relationship to teacher beliefs and classroom practices; and (b) a quality review of a rigorous mathematics standard.;Less than 6% of the students demonstrated retrieval of 80% or more of the 10 addition and 8 subtraction facts sampled in one-on-one student interviews during the last 4 to 6 weeks of first grade. Even among the 125 students from top-decile schools, less than 11% of the students made progress toward the standard equivalent to their progress through the school year. Second-language learners attending high-SES schools achieved the highest performance of any subgroup (M = 61.78%, SD = 29.93%), with 36% of those students retrieving 80% or more of the basic facts.;Teachers reported high levels of state-approved textbook reliance. However, textbook reliance was negatively correlated with basic facts retrieval, and positively correlated with student use of counting strategies to solve basic fact problems. Textbook reliance was also negatively correlated with a measure of number sense proficiency that included place value and word problems.;Teachers also reported implementing, on average, 15 additional instructional activities each week to help students learn their facts; only 1, on average, was reported to be focused on the goal of memorization. Several negative correlations between these instructional strategies and students' basic facts retrieval suggest that teachers may benefit from professional development targeted at basic facts teaching and learning.;Based on low teacher acceptance of the standard, questionable instructional effectiveness, evidence of bias, and a failure to demonstrate developmental appropriateness, California's first-grade basic facts standard scored zero out of four on a test of standards quality. Several recommendations for student support and standards review and revision are discussed.