This study examined the efficacy of a Tier 2 kindergarten mathematics intervention program, ROOTS, focused on developing whole number understanding for students at risk in mathematics. A total of 29 classrooms were randomly assigned to treatment (ROOTS) or control (standard district practices) conditions. Measures of mathematics achievement were…

This article introduces the formative assessment probe--a powerful tool for collecting focused, actionable information about student thinking and potential misconceptions--along with a process for targeting instruction in response to probe results. Drawing on research about common student mathematical misconceptions as well as the former work of…

This study examined the efficacy of a Tier 2 kindergarten mathematics intervention program, ROOTS, focused on developing whole number understanding for students at risk in mathematics. A total of 29 classrooms were randomly assigned to treatment (ROOTS) or control (standard district practices) conditions. Measures of mathematics achievement were…

The language that students use with whole numbers can be insufficient when learning integers. This is often the case when children interpret addition as "getting more" or "going higher." In this study, we explore whether instruction on mapping directed magnitudes to operations helps 88 second graders and 70 fourth graders solve…

It has long been debated whether interpretation should be performed only from a foreign language to the mother tongue or whether it should be performed from the mother tongue to a foreign language. Those in favor of the foreign to native language direction posit that such directionality allows the interpreter to produce more natural target…

Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual…

Transitioning from teaching whole number operations to teaching fraction operations can prove difficult, even for the seasoned mathematics teacher. However, with effective literacy practices, teachers can seamlessly shift their students to learning the rules for fractions. The implications can be a mastery of mathematical language used to describe…

Differentiating instruction can be difficult, however, when higher performing students yearn to be stretched and lower performing students benefit from scaffolded support. One way to meet these students' learning needs and everyone in-between is to embrace the notion of novel exploration in support of critical school mathematics concepts. Novelty…

National and state assessments show that English language learners (ELs) in elementary and secondary grades score lower in mathematics compared with their matched English proficient peers (EPs). To provide information on strategies for enhancing learning opportunities for ELs in language inclusive classrooms, we analyze the efficacy of…

Practice: An Inquiry-Based Mathematics Activities Module (IBMAM) was developed in accordance with the developmental characteristics, interests, needs, and expectations of preschoolers. The aim of the study was to determine the effect of the IBMAM on preschoolers' numbers and operations skills. A quasi-experimental method, which was a…

The history of the number zero is an interesting one. In early times, zero was not used as a number at all, but instead was used as a place holder to indicate the position of hundreds and tens. This article briefly discusses the history of zero and challenges the thinking where divisions using zero are used.

The problem of adverse effects of prior knowledge in mathematics learning has been amply documented and theorized by mathematics educators as well as cognitive/developmental psychologists. This problem emerges when students' prior knowledge about a mathematical notion comes in contrast with new information coming from instruction, giving rise to…

In this article, we revisit the concept of strong differentiability of real functions of one variable, underlying the concept of differentiability. Our discussion is guided by the Straddle Lemma, which plays a key role in this context. The proofs of the results presented are designed to meet a young audience in mathematics, typical of students in…

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes…

Mathematical learning not only produces students who succeed in mathematical and procedural calculations but also develops religious thinking. Realistic mathematics education with the context of Islamic values makes students can imagine, which is one of the right ways to develop the skills of students' creativity, collaboration, and communication.…