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This paper presents the early results of an experiment involving a class of elementary student teachers within the context of their mathematics preparation. The motivation of the exercise centered on giving them an experience with mathematical research at their own level and ascertaining its impact on their attitudes and beliefs. The students spent the first month working on open-ended geometrical topics. In the second month, working alone or in groups of up to four, they chose one or more of these topics then worked on a problem of their own design. The students spent the class time developing their ideas using strategies such as generating examples and non-examples, generalising, etc. Reference to books was not accepted as a research tool, but the instruction team monitored student progress and was available for questions. [For complete proceedings, see ED489538.]

This paper reports on the use of the RAMR framework within a curriculum project. Description of the RAMR framework's theoretical bases is followed by two descriptions of students' learning in the classroom. Implications include the need for the teacher to connect student activities in a structured sequence, although this may be predicated on the teacher's own structural understanding of mathematics.

"Counting On" is a systemic mathematics program that targets low achieving students in the final year of government elementary and the first year of government secondary schools through the professional development of their teachers. During 2000, "Counting On" was implemented in 40 secondary schools, involving more than 600 students, 120 school teachers, and 40 district mathematics consultants. In 2001, the implementation was extended to approximately 80 secondary schools and 80 final year elementary classes which "feed" these secondary schools, involving some 1,400 students, 320 teachers, and the 40 district mathematics consultants. This paper reports on evaluations of the program in 2000 and 2001, with particular reference to students' movement across the levels of conceptual development in place value contained in the numeracy framework which underpins the program. (Author)

"Counting On" is a systemic mathematics program that targets low achieving students in the final year of government elementary and the first year of government secondary schools through the professional development of their teachers. During 2000, "Counting On" was implemented in 40 secondary schools, involving more than 600 students, 120 school teachers, and 40 district mathematics consultants. In 2001, the implementation was extended to approximately 80 secondary schools and 80 final year elementary classes which "feed" these secondary schools, involving some 1,400 students, 320 teachers, and the 40 district mathematics consultants. This paper reports on evaluations of the program in 2000 and 2001, with particular reference to students' movement across the levels of conceptual development in place value contained in the numeracy framework which underpins the program. (Author)

In mathematics, the expectation to set up and solve word problems emerges as early as kindergarten; however, many students who experience mathematics difficulty (MD) and dual-language learners often present with specific challenges in this area. To investigate why these populations experience word-problem difficulty, we examined the word, problem solving and oral explanations of third-grade dual-language learners (DLLs; n = 40) and non-DLLs (n = 40), all of whom were identified as experiencing MD. Students solved five additive word problems and provided oral explanations of their work, which were transcribed and coded for the number of words in each explanation, type of mathematics vocabulary terms used, inclusion of correct numbers in explanations, and descriptions of addition or subtraction. We identified no significant differences in word-problem scores between DLLs and non-DLLs with MD. For both DLLs and non-DLLs, students who answered problems correctly used more words in each explanation and used more mathematics vocabulary terms within their explanations. For incorrectly answered problems, the most common mistake for both DLLs and non-DLLs involved using the incorrect operation to solve the problem. [This article was published in "Learning Disability Quarterly" (EJ1323542).]

The purpose of this study was to examine the word-problem performance and strategies utilized by 3rd-grade students experiencing mathematics difficulty (MD). We assessed the efficacy of a word-problem intervention and compared the word-problem performance of students with MD who received intervention (n=51) to students with MD who received general education classroom word-problem instruction (n=60). Intervention occurred for 16 weeks, 3 times per week, 30 min per session and focused on helping students understand the schemas of word problems. Results demonstrated that students with MD who received the word-problem intervention outperformed students with MD who received general education classroom word-problem instruction. We also analyzed the word-problem strategies of 30 randomly-selected students from the study to understand how students set up and solve word problems. Students who received intervention demonstrated more sophisticated word-problem strategies than students who only received general education classroom word-problem instruction. Findings suggest students with MD benefit from use of meta-cognitive strategies and explicit schema instruction to solve word problems. [This paper was published in "Journal of Mathematical Behavior" v58 Article 100759 2020.]

As part of the Writing Across the Curriculum movement, teachers are asked to integrate writing into their teaching of mathematics; however, this can be a difficult task given that most elementary school teachers have had little experience using writing as a tool to learn and communicate their understanding of mathematics. To give students in my mathematics content courses the valuable experience of writing mathematical explanations, writing has become an integral part of my courses for preservice teachers. The paper that follows focuses on how I support strong written explanations in my mathematics content courses for elementary school teachers.

This study investigates how successful the Urban Alternative Preparation Program (UAPP) integrated mathematics/methods sequence was at changing the beliefs and practices of preservice teachers in the program. The program is grounded in constructivist learning theory and promotes practices that support that perspective. A group of eight students who held non-education undergraduate degrees and were preparing to become certified in a K-5 urban setting participated in the study. Results indicate that they demonstrated beliefs and practices that were more consistent with the philosophy of reform and a strong resilience in their newfound beliefs and practice. (KHR)

This report examines which instructional components (e.g., visual representations, use of number lines, teaching and using of mathematical language) and study features (e.g., group size, interventionist training) may have contributed to the effectiveness of intervention. In choosing to focus on instructional components and study features, the findings have the capacity to inform state and district leaders, as well as teachers providing intervention, on which instructional components are necessary for a rational numbers intervention to be effective. Studies that were used in the meta-analysis were ones that focused on teaching rational numbers concepts to students experiencing mathematics difficulties in Grades 3 through 9. Approximately 1,500 studies were identified and screened, leaving 77 reports to be screened more in-depth for relevance. Those still eligible were then screened for rigor by applying the What Works Clearinghouse (WWC) evidence standards. A total of 26 studies with 4,237 unique participants from 30 independent samples were included in the meta-analysis. Results from the meta-analysis suggest that intervention programs devoting time to the teaching and use of mathematical language can substantially enhance outcomes. Mathematical language is a type of abstract academic language (terms such as "equivalent," "reciprocal," "circumference") that helps students learn mathematics concepts more precisely. When students understand and use mathematical language, it is believed that the students will more deeply understand the mathematics they are learning.

138 p. : 18 cm

This systematic review and meta-analysis appraised and synthesized mathematics interventions research addressing rational number concepts for students with mathematics difficulties (MD) in Grades 3-9. Included studies (n = 28) meet the What Works Clearinghouse Group Design standards (Version 4.0) for study quality. Across all studies, we found significant mean effects (g = 0.68) favoring intervention. Understanding which instructional components within interventions are associated with effects was a fundamental purpose of the study. Random-effects meta-regression models with robust variance estimation (RVE) were used to examine which instructional components moderated effects. The teaching and use of accurate mathematical language emerged as significant (b = 0.50, p = 0.042) when controlling for other instructional components (visual representations, review, student explanations, and fluency building activities) and three control variables (group size, duration, nature of the control). Intervention characteristics and study design features were also explored through moderator analysis. Group size, duration, nature of the control, type of measure, interventionist, provision of ongoing training, and grade level emerged as significant moderators (p < 0.05). [For a previous version of this report, see ED612822.]