A Title I elementary school in New York City faced a challenge in supporting students in Grade 3 to Grade 5 who did not meet state proficiency standards in mathematics. The student body of approximately 300 was 80% Black and Brown students, with 40% of students identified as English language learners or students with disabilities. The assistant…

The Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) highlight the mathematical habits that educators should be fostering in mathematics classrooms throughout K-grade 12 education. That argumentation and discourse are important components of developing mathematically proficient…

This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…

The maturation of multiplicative thinking is key to student progress in middle school as rational number, ratio, and proportion concepts are encountered. But many students arrive from the intermediate grades and falter in developing this essential disposition. Elementary students have historically learned multiplication and division as operation…

This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures…

The purpose of this study was to provide teachers and principals with concrete evidence to demonstrate that weekly math homework increases academic performance in math. This study focused mainly on homework's effects on quiz scores. It compared quiz scores of students who did homework with those who did not. The subjects of this study included 21…

Many teachers bring caterpillars into their class for their students to see the transformation from caterpillar to butterfly. This is exciting and educational, but more can be done using Monarchs across the curriculum. This article describes an integrated butterfly unit for students in grades four to six that starts with identifying the Monarch…

Presents an alternative pedagogy implicit in Imre Lakatos's "Proofs and Refutations: The Logic of Mathematical Discovery." Lakatos reveals that learning mathematics is a discourse-laden activity in which it is acceptable, if not preferable, to refute conjecture. Provides examples of using a Lakatosian approach in an elementary classroom.…

Presents a mathematics activity using hand-held technology that can be used with elementary school students. Uses graphing calculators and calculator-based laboratories in this activity. (Contains 11 references.) (ASK)

Analyzes the individual and collective activities of fourth grade students while trying to explain a school fellow's mistake in the use of a geometrical schema for the sunshadows phenomenon. Aims at detecting productive links between context-related argumentation and mathematical modeling as well as discussing their relevance for mathematics…

This six month study investigated the similarities and differences between 137 fourth graders' understanding of and reasoning about multiplication, division, and proportion tasks. All students were administered a pretest mid-year and a posttest at the end of year. A sample of 18 students was interviewed individually on tasks involving reasoning…

Schumacher and Nash (1991) theorize that writing provides an avenue for people to reorganize their knowledge. Kieren (1988) is one of several researchers who theorize that children's school fraction experiences should begin with personal knowledge of fractions. The purpose of this study was to determine whether or not children who engaged in…

This book provides a resource for mathematics teachers to understanding the National Council of Teachers of Mathematics' (NCTM) standards and implementing these standards in their teaching. Five standards are overviewed: (1) number and operation; (2) algebra; (3) geometry; (4) measurement; and (5) data analysis and probability. Lesson plans are…

The purpose of the Idaho Direct Mathematics Assessment (DMA) is to measure Idaho students' mathematical problem-solving skills, including their ability to apply basic skills to problem-solving situations as stated in the Idaho Achievement Standards document. Problem solving is valued as an essential tool for success in a complex, modern world. The…

Presents two vignettes of mathematics lessons and describes fourth-grade students' discussions of fractions, percents, decimals, time, and money while investigating the various interpretations of the word "quarter." (ASK)