This is a companion piece to "Professional Learning Community: Improving Mathematical Problem Solving for Students in Grades 4 through 8. Facilitator's Guide. REL 2019-002" (ED595201). It contains handouts to accompany each of the sessions included in the facilitator's guide.

There is no doubt that a lesson plan is a necessary product of Lesson Study. However, the collaborative work among teachers that goes into creating that lesson plan is largely under-appreciated by non-Japanese adopters of Lesson Study, possibly because the effort involved is invisible to outsiders, with our attention going to its most visible…

This study sought to a better understanding of the construct of problem solving in technology-rich environments and the effect of literacy and numeracy on problem solving. Data used in this study were drawn from Programme for the International Assessment of Adult Competencies US data which includes 5010 completed cases and a total of 1326…

The development of multiple solutions for a given problem is important for learning mathematics. In the present intervention study, we analyzed whether prompting students to construct multiple solutions (more precisely: prompting them to apply multiple mathematical procedures to real-world problems) and prior self-efficacy influenced students'…

The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126…

The purpose of this study was to investigate eight preservice middle and high school mathematics teachers' solution strategies when solving single and multiple proportion problems. Real-world missing-value word problems were used in an interview setting to collect information about preservice teachers' (PSTs) reasoning about proportional…

There is a great deal of overlap between the set of practices collected under the term "computational thinking" and the mathematical habits of mind that are the focus of much mathematics instruction. Despite this overlap, the links between these two desirable educational outcomes are rarely made explicit, either in classrooms or in the…

In this study, we investigate sixth, seventh, and eighth grade students' achievement in nonlinear (quadratic or cubic) proportional problems regarding length, area, and volume of enlarged figures. In addition, we examine students' solution strategies for the problems and obstacles that prevent students from answering the problems correctly by…

This study investigated the pattern problems posed by middle school mathematics preservice teachers using multiple representations to determine both their pattern knowledge levels and their abilities to transfer this knowledge to students. The design of the study is the survey method, one of the quantitative research methods. The study group was…

The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that "enable" year 10/11 students to…

This study examined the effects of two training methods (interest-based and traditional) used to improve math word problem performance of middle school students with and without learning disabilities, as measured by the Herr Scale of Mathematical Word Problem Solving Situations. Students were randomly assigned to one of the two treatment groups:…

This study was conducted during the first semester of 2016, from March 21st to June 30th, with 104 students, in eight educational centers or "polos," in the states of Minas Gerais and São Paulo. Previously, these mathematics teacher education students had no opportunity to study in higher education in Brazil. They were enrolled in a…

Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers' conceptions of student arithmetic word problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe…

In the era of multi-tiered system of support approach to learning, identifying mathematical interventions that have been found to be effective for students who are struggling academically is imperative. Given the divide between instructional approaches in general and special education mathematical teaching approaches, it is important to bridge the…

Mathematics itself is a living and creative act (Boaler, 2008), and mathematicians themselves often collaborate in their work (Burton, 2004). What, then, is holding school mathematics back? Are educators so conditioned to expect the act of mathematizing in school to proceed in a certain abstract, formalized way that they are neglecting other means…