In this synthesis, we analyzed 10 prealgebraic reasoning interventions for students with mathematics difficulty (MD) in Grades 6 through 8. All interventions focused on one or more prealgebraic concepts including integer operations, algebraic expressions and equations, and functions. Of the 10 intervention studies, six employed single-case design…

This study is a series of Didactical Design Research in prospective analysis stage to comprehensively identify some obstacles in learning negative integer in order to capture how the learning process used by teachers and how the impact on students in understanding the concept of negative numbers. This research is a case study administered to…

Background: Poor mathematics performance in South Africa is well known. The COVID-19 pandemic was expected to exacerbate the situation. Aim: To investigate Grade 7 learners' mathematical knowledge at the end of primary school and to compare mathematical performance of Grade 7 and 8 learners in the context of the pandemic. Setting: Data were…

A design experiment with 18 students in a regular seventh grade math class was conducted to investigate how to differentiate instruction for students' diverse ways of thinking during a 26-day unit on proportional reasoning. The class included students operating with three different multiplicative concepts that have been found to influence rational…

Some people recognize a palindrome when they see one, however fewer realize that a palindrome is a special case of a pattern and that these patterns are all around. Palindromes frequently occur in names, both of vehicles and people, and in music. The traditional mathematical curriculum has often left palindromes out of the common vernacular. Where…

This research study investigates the ability of students to tackle the solving of unique mathematical problems in the domain of numerical series, verbal and formal, and its influence on the motivation of junior high students with learning disabilities in the Arab sector. Two instruments were used to collect the data: mathematical series were…

Motivating middle school students to learn can be challenging. One proven method for doing so is through an integrated curriculum. Educational philosophers and curriculum theorists have long noted the benefits of an integrated curriculum, which recognizes that the subject areas within the curriculum are connected to one another and to the real…

Many students experience great difficulty understanding the meaning of fractions. For many students who have spent their early mathematics lessons focusing on counting (whole) numbers, recognising that there are many numbers between those whole numbers called fractional numbers, is quite revolutionary. The foundation of understanding fractions is…

Tasks to Advance the Learning of Mathematics (TALMs) were developed to stimulate grades 5-8 students' curiosity about complex mathematical relationships, inspire them to reason abstractly and quantitatively, encourage them to consider and create alternative solution approaches, develop their skills to persuade others about the viability of one…

At grade 7, Common Core's content standards call for the use of long division to find the decimal representation of a rational number. With an eye to reconciling this requirement with Common Core's call for "a balanced combination of procedure and understanding," a more transparent form of long division is developed. This leads to the…

The aim of this study is to study learning the positional ten base notation by the increase of students' test scores during the learning study process. Five teachers, one researcher and 53 students participated. Three research lessons in three different groups of students were conducted. The improvement in the third lesson (C) correlates with the…

This article presents the results of a 7th-grade classroom teaching experiment that supported students' understanding of integer addition and subtraction. The experiment was conducted to test and revise a hypothetical learning trajectory so as to propose a potential instructional theory for integer addition and subtraction. The instructional…

If the ability to reason proportionally seems to be a good indication of likely success in further mathematical pursuits (Lamon, 1999), how do children develop this ability, and how can teachers facilitate this? In this present study, six ratio/rates task-based assessment questions were trialled on ten students from Grades 5 to 9 in an attempt to…

The combined seventh-grade and eighth-grade class began each day with a mathematical reasoning question as a warm-up activity. One day's question was: Is the product of two odd numbers always an odd number? The students took sides on the issue, and the exercise ended in frustration. Reflecting on the frustration caused by this warm-up activity,…

Supporting a productive discourse is an important element of reform teaching, as it gives students opportunities to understand mathematical reasoning. In this study, the practices of an expert seventh-grade mathematics teacher are described to illustrate how she created and sustained a genuine mathematical discourse environment during the teaching…