This study examined how two small-group discourse types (Reflective and Exploratory) supported the inclusion and enacted levels of cognitive demand of students who typically struggle with mathematics in real-world, task-based assessment activities. The study focused on 11 fifth-grade students within a larger study involving 97 fifth-grade students…

Twenty-four Grade 5 students participated in clinical interviews where they solved integer multiplication number sentences. Drawing on the theoretical perspective of strategies that students use with whole number multiplication and integer addition and subtraction, we describe the strategies that students employ when negative integers are…

Identifying components of teaching that make a difference in children's learning is an ongoing challenge in our field. Focusing on teaching that is responsive to children's fraction thinking, we decomposed responsiveness into the instructional practices of questioning to support and extend children's thinking, noticing children's thinking, and…

This paper describes how fifth-grade English Learner students (ELs) in an urban school district develop the mathematics register during a problem-solving lesson. It provides examples of students' work to illustrate how they use the mathematics register to communicate their mathematical ideas orally and in writing. The teacher implemented teaching…

In this study, I investigated Grade 4 and 5 students' emotions while they engaged in the exploration of unsolved mathematics problems, including parts of the Graceful Tree Conjecture. Ten students from an after-school program in the Midwest participated in seven task-based interviews. The students exhibited a variety of emotions throughout the…

This paper focuses on Emergent bilinguals (EBs) who traditionally face unequal opportunities to learn mathematics, harming their identities. The purpose of this paper is to illustrate how a fifth grade teacher cultivated the development of her EBs' mathematical identities by giving them opportunities to participate in cognitively demanding…

In this case study, we examine the usage of language -- how teachers used and regulated their language when teaching English language learners (ELLs) with learning disabilities (LD) how to solve mathematics multiplication problems. We focus on types of scaffolds used by teachers to identify how scaffolding helps ELLs with LD build better…

In this study we investigated the effect of the request to reword the text of problematic word problems on the occurrence of realistic answers. We proposed the activity of rewording word problems to fifth grade pupils either working individually or in dyads. We found that the rewording the problems while working individually had no effect, while…

We present the results of a study analysing the cooperative behaviour of fifth-grade student pairs when they have to overcome a difficulty (a barrier) in a mathematical problem task. As analysing method we used content analysis as well as frequency-tests (chi-squared test, CFA, Freeman-Halton-test). Our results help to confirm and elaborate the…

In this study, how fourth- to sixth-grade children perform measurement estimation was investigated. The data were collected by a measurement estimation task that contained linear and area estimations and interviews from 72 children, each in one fourth- (n = 21), fifth- (n = 32), or sixth-grade (n = 19) class at local public elementary schools in…

In this paper I focus on observations made regarding students mimicking of each other's gestures in face-to-face conversation while problem solving. The data supports the idea that the students may use such gestures to subconsciously signal acceptance. Through talk, gesture, prosody, and intonation, combined with context, the interlocutors may…

Both additive and proportional reasoning are types of quantitative analogical (QA) reasoning. We investigated the development and nature of primary school children's QA reasoning by offering two missing-value word problems to 3rd to 6th graders. In one problem, ratios between given numbers were integer, in the other ratios were non-integer. These…