RECOGNISE FRACTIONS OF HUNDREDTHS AND DECIMALS

1980

The Michigan Educational Assessment Program (NEAP) staff developed strategies to train teachers and principals to use state assessment results for improving academic achievement in their schools. Two local uses of the state assessment results are (1) using the results of grades 4, 7, and 10 with the students tested, and (2) using the results to review curricula in the previous grade levels. Samples of materials developed for each type of use are appended, and include instructional support materials for mathematics, pamphlets for preparing school staffs to provide individual student results to provide individual student results to parents, plans for preparing for a utilization of BM test results workshop, and a model for utilization of NEAP test results. Presentation of the utilization model is planned for three sessions: Session I examines the test results and identifies present needs: Session II deals with curriculum and instructional planning: and Session III is devoted to decision making and setting goals. Because these methods were developed by observation of what does work in schools and because the techniques were geared to the resource restraints of local schools, they can be applied in a variety of settings. (RL) Introduction and Background

Frontiers in human neuroscience, 2014

Decimal fractions comply with the base-10 notational system of natural Arabic numbers. Nevertheless, recent research suggested that decimal fractions may be represented differently than natural numbers because two number processing effects (i.e., semantic interference and compatibility effects) differed in their size between decimal fractions and natural numbers. In the present study, we examined whether these differences indeed indicate that decimal fractions are represented differently from natural numbers. Therefore, we provided an alternative explanation for the semantic congruity effect, namely a string length congruity effect. Moreover, we suggest that the smaller compatibility effect for decimal fractions compared to natural numbers was driven by differences in processing strategy (sequential vs. parallel). To evaluate this claim, we manipulated the tenth and hundredth digits in a magnitude comparison task with participants' eye movements recorded, while the unit digits r...

Decimals are among the difficult subjects for the students because of its abstract nature. Therefore, the aim of this study is to develop instructional materials for students based on one of the four-stage models of constructivist approach related to the unit of “decimals”. With this aim, a worksheet, analogy map and conceptual change text on the unit of decimals were developed. Case study method was used in the study. A pilot study was conducted with 32 6th graders studying in an elementary school in Trabzon in order to use the instructional materials in the classes more effectively and to test their feasibility. At the end of this preliminary study, the students were determined to find the materials effective, visual and interesting. Therefore, it’s recommended to use the materials developed during the course in mathematics classes and to develop similar materials for other subject matters.

Studies reveal that students as well as teachers have difficulties in understanding and learning of decimals. The purpose of this study is to investigate students' as well as pre-service teachers' solution strategies when solving a question that involves an estimation task for the value of a decimal number on the number line. We also examined the pre-service teachers' anticipation of students' misconceptions and difficulties for the given task. To conduct our analysis, we conducted interviews with three 5 th and three 6 th grade students, and eight preservice teachers. During the interviews we asked them to solve the question and explain their solution strategies. The findings of the study indicate that students and pre-service approach this problem in different ways. However, both groups have a tendency to think of decimals successively and indicate precise answers rather than specifying a range of possible values. We also observed the preservice teachers could only partially anticipate the misconceptions and difficulties faced by the students.

Studies reveal that students as well as teachers have difficulties in understanding and learning of decimals. The purpose of this study is to investigate students’ as well as pre-service teachers’ solution strategies when solving a question that involves an estimation task for the value of a decimal number on the number line. We also examined the pre-service teachers’ anticipation of students’ misconceptions and difficulties for the given task. To conduct our analysis, we conducted interviews with three 5th and three 6th grade students, and eight pre-service teachers. During the interviews we asked them to solve the question and explain their solution strategies. The findings of the study indicate that students and pre-service approach this problem in different ways. However, both groups have a tendency to think of decimals successively and indicate precise answers rather than specifying a range of possible values. We also observed the pre-service teachers could only partially anticipate the misconceptions and difficulties faced by the students.

Journal for Research in Mathematics Education, 1989

Learning and instruction, 2010

Learning about decimal fractions is difficult because it requires an extension of the number concept built on natural numbers. The aim of the present study was to investigate developmental changes in children's misconceptions in decimal fraction processing. A large sample of children from Grades 3 to 6 performed a numerical comparison task on different categories of pairs of decimal fractions. The success rate and the type of error they made varied with age and categories. We distinguished the impact of the value of the digits from the impact of the length of the fractional part on children's pattern of responses. Although both kinds of impact affected the success rate, the digit values had a stronger impact and were mastered later than the length. Our results also showed that a zero just after the decimal point was understood better and earlier than a zero at the end of the fractional part of a number. Cluster analysis was conducted to determine groups of children who answered similarly regarding the response type across the various categories of decimal fractions. To interpret the data the conceptual change framework was used.

Journal of Educational Research, 2016

Teachers need more clarity about effective teaching practices as they strive to help their low-achieving students understand mathematics. Our study describes the instructional practices used by two teachers who, by value-added metrics, would be considered "highly effective teachers" in classrooms with a majority of students who were English learners. We used quantitative data to select two fifth-grade classrooms where students, on average, made large gains on a mathematics achievement test, and then examined teaching practices and contextual factors present in each classroom. Participants included two teachers from a mid-Atlantic district and their students who were 67% English learners and 68% economically disadvantaged. We found that the use of multiple representations of mathematics concepts, attention to vocabulary building, individual and group checks for understanding and error analysis were prevalent practices in both high gains classrooms. Also, class sizes ranged from 12-19 students. Discussion focuses on whether observed practices are aligned with recommended teaching practices for EL students.

International Group For the Psychology of Mathematics Education, 2003

Informed by theory and research in inquiry-based classrooms, this paper examines how classroom practices support students' understanding of decimals. Data from a six-month teaching experiment, based on the work of use of percentages and metric measure as visible representations for students' emerging understanding of decimals, indicated that understanding was significantly influenced by a classroom climate that supported sense making. Sensing, established by a shared expectation, was used and extended in the form of sociomathematical norms associated with mathematical argument and authority.