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We describe a project to formalize Galois theory using the Lean theorem prover, which is part of a larger effort to formalize all of the standard undergraduate mathematics curriculum in Lean. We di...

In 2010 a mathematics curriculum was introduced in Irish second level schools entitled ‘Project Maths’ (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). Report of the Project Maths implementation support group. https://www.education.ie/en/Publications/Policy-Reports/Report-of-the-Project-Maths-Implementation-Group.pdf]. This paper aims to examine the performance of 1st year undergraduate students’ procedural and problem solving skills after the introduction of PM. A diagnostic test was developed to determine students’ skills in each area and findings demonstrated that students perform statistically significantly better in the procedural skills in mathematics when compared to problem solving skills. These findings raise concerns around the lack of anticipated improved problem solving skills of a cohort of students exposed to this style of teaching and learning. The paper raises discussion surrounding the intended and actual teaching and learning taking place in second level classrooms along with consideration for the potential role of learned helplessness and the literacy issues. Recommendations are made for follow up qualitative research with stakeholders in mathematics education to better understand the ‘why’ of the results presented here.

This study investigated the role of the bar model method, a significant aspect of the Singapore mathematics curriculum, in the remediation of seventh-grade students’ errors on algebra word problems...

This article describes the authors’ experiences developing and implementing an innovative curriculum connecting mathematics and the biological sciences. It describes the original plan, the modifica...

Learning to solve arithmetic word problems is an essential part of the primary school mathematics curriculum. The success of word-problem solving was previously found to relate to reading comprehen...

The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design ...

Randomized evaluations of educational technology produce log data as a bi-product: highly granular data student and teacher usage. These datasets could shed light on causal mechanisms, effect heterogeneity, or optimal use. However, there are methodological challenges: implementation is not randomized and is only defined for the treatment group, and log datasets have a complex structure. This paper discusses three approaches to help surmount these issues. One approach uses data from the treatment group to estimate the effect of usage on outcomes in an observational study. Another, causal mediation analysis, estimates the role of usage in driving the overall effect. Finally, principal stratification estimates overall effects for groups of students with the same "potential" usage. We analyze hint data from an evaluation of the Cognitive Tutor Algebra I curriculum using these three approaches, with possibly conflicting results: the observational study and mediation analysis suggest that hints reduce posttest scores, while principal stratification finds that treatment effects may be correlated with higher rates of hint requests. We discuss these mixed conclusions and give broader methodological recommendations., Forthcoming, Journal of Research in Educational Effectiveness

The local needs and circumstances in curriculum revision often necessitate improvements in the quality of education. However, problems associated with the revision of curricula in developing countr...

For teachers to integrate ethnomathematics approaches, it is essential to understand their views related to the implementation challenges of such approaches. In schools, teachers held previous view...

Early career teachers (ECTs) face unprecedented pressure to fulfill expectations of ‘highly effective’ teachers within their first few years of teaching. Lesson planning is an important precursor t...

Since problem solving became one of the foci of mathematics education, numerous studies have been performed to improve its teaching, develop students’ higher-level skills, and evaluate its learning...

Textbooks are a widely used educational intervention that can affect student achievement, and the marginal cost of choosing a more effective textbook is typically small. However, we know little abo...

This article examines the role that replication research has played in the development and refinement of mathematics interventions for learners with extensive support needs. By highlighting 16 rese...

This paper is intended to provide a source of critical and theoretical reflection on the current mathematics educational objectives for Indigenous students in Australia, which are premised on accep...

This paper argues that there is a gap in the research on teaching and learning mathematics, and thus a need for research into effective teaching practices. From a selective review of literature, re...

This paper results from programming of Indigenous Logix: Mathematics|Culture|Environment (IndigiLogix). IndigiLogix’s intention is to increase Indigenous students’ love for mathematics as well as c...

This study analyzed how the earliest teaching and learning of probability was organized in Singapore, the US, and Indonesia through an analysis of textbook as an intended mathematics curriculum. An...

We have integrated computer programming instruction into the required courses of our mathematics major. Our majors take a sequence of four courses in their first 2 years, each of which is paired with a weekly 75-minute computer lab period that has a dual purpose of both computationally exploring the mathematical concepts from the lecture portion of the course, while simultaneously teaching programming fundamentals. Building on this foundation, we give significant programming assignments to our upper-division students, requiring them to regularly use and apply their programming skills to investigate the mathematical topics.

To promote and facilitate the teaching of math modeling throughout the K–16 setting, the Consortium for Mathematics and Its Applications and the Society for Industrial and Applied Mathemati...

In many countries, in contemporary math curricula, particularly in early childhood and childhood classrooms, it is considered crucial to encourage children to show their work, to concretely represe...

One argument for the use of contexts in mathematics instruction has been that contexts can serve as anchors that support students in understanding and recalling mathematical ideas. Evidence of this...

We consider the use of projects in math courses as a mechanism for promoting coding, communication, and interdisciplinary application of math skills. Final projects play an important role, ...

First-grade mathematics curriculum has been typically constructed to emphasize the development of whole number and operations. Topics addressed to a lesser extent include algebraic thinking, measur...

Mathematics faculty created a model for intermediate algebra integrating principles from the science of learning. The redesigned curriculum revolved around two big ideas (solving and graphi...

Trends in curriculum reform recognise the need to develop skills and competencies in addition to specifying what knowledge should be taught and when. However, a balance between skills and knowledge...

Mathematical reasoning and tools are intrinsic to science, yet the close and dependent relationship science has to mathematics is not reflected in either school education or science education research. This paper asks what the barriers are to a mutually beneficial relationship between the two disciplines. A two-phase qualitative interview study was used to explore the relationship between school science and mathematics education through the perspectives of science and mathematics education policy-makers and of teachers in departments which are unusual in collaborating. In total there were 36 participants. Interview data were analysed using thematic analysis. Findings show that there is an asymmetry in the dependency between school science and mathematics: science is dependent on mathematics but the reverse is not true. We discuss three consequences of this asymmetric dependency: there is greater benefit for science from any collaboration; ‘maths blame’ can arise from science teacher frustration; and science educators may believe they should have some ownership of the mathematics curriculum. Asymmetry of dependency, and therefore of benefit, will make it very difficult for mathematics and science to work together in a way which is genuinely mutually beneficial.

Two common interest-enhancement approaches in mathematics curriculum design are illustrations and personalization of problems to students’ interests. The objective of these experiments is to test a variety of illustrations and personalization approaches. In the illustrations experiment, students (N = 265) were randomly assigned to lessons with story problems containing decorative illustrations, contextual illustrations, diagrammatic illustrations, misleading illustrations, or no illustrations (only text; control). Students’ problem-solving performance and attitudes were not affected by illustration condition, but learning was better in the control compared to contextual illustrations. In the personalization experiment, students (N = 223) were randomly assigned to story problems that were either personalized based on: a survey of their interests, their choice of interest topics, a randomly-assigned interest topic, or the original non-personalized story problem (control). The findings indicated there were benefits for choice personalization both for performance in the problem set as well as on a later learning assessment.

Scholars propose that contextual problems can be used to ground students’ understanding of mathematical ideas, and recent curricular trends have resulted in a plethora of resources that int...

This paper explores the challenge of determining the mathematics curriculum for students with Down syndrome in our digital age where the tools of mathematics including electronic calculators and sm...

The authors investigated the effect of a mathematical curriculum (CU) developed based on verbal and practical activities on the mathematical competency (MC) and learning behaviors (LB) of preschool...

This paper deals with the nature of teaching mathematical thinking and presents a case study of a single Japanese lesson where the characteristics of mathematical thinking and the teaching thereof ...

The quantum of instruction time allocated to curriculum subjects such as mathematics facilitates greater exposure to knowledge and skill development, leading to higher levels of achievement. There ...

At the University of Hartford we transformed our approach to Calculus I – moving it away from a lecture-dominant format to one that focuses squarely on students solving problems and discussing and ...

Using a national sample of students’ writing from the National Study of Writing Instruction, this study examines the current state of writing in the mathematics classroom and the extent to which en...

One of the challenges of implementing a new curriculum is how to bridge the gap between the underlining principles of the curriculum and the cultural and social orientations of the society ...

This article presents a critical action research study of six participants who reflected on their experiences and practices of digital resources in teaching Grade 12 mathematics Curriculum and Asse...

Elementary mathematics curriculum materials can serve as a lever for instructional change. In this paper, we promote a particular kind of instructional change: supporting teachers in learning to in...

In an experimental study to explain the effect of structured Building Block Play with LEGO™ bricks on 6-year-old student mathematics achievement and in the areas of logical thinking, divergent thin...

The study explored the contributing factors in implementing the learning study approach in Tanzanian secondary schools. Three mathematics teachers formed a learning study group, guided by the varia...

Epistemology is a conceptual template for how we think about the world, and the study of how we come to know the world around us. The world does not dictate unequivocally how to interpret it. This ...

In this paper, we present findings from a preliminary analysis of transcript data in the High School Longitudinal Study (HSLS:09), a large-scale longitudinal investigation of academic achievement among U.S. high school students. Using proportional flow diagrams of course-taking patterns, we illustrate differences in calculus completion associated with non-malleable student characteristics such as ethnicity, gender, and socioeconomic status (SES), as well as malleable student characteristics, such as knowledge of mathematics in ninth grade, the level of mathematics course they take in ninth grade, and self-efficacy. Confirming and extending findings from prior literature, we conclude that “tracks” through high school mathematics curriculum, together with students' ethnicity, SES, and self-efficacy, converge as important factors associated with which of the approximately 19% of high school students complete calculus in high school.

This study examines the effectiveness of integrating geography into existing math and science curriculum to teach climate change and sea level rise. The desired outcome is to improve student performance in all three subjects. A sample of 120 fifth graders from three schools were taught the integrated curriculum over a period of two to three weeks. They were given a pretest and posttest comprised of questions measuring knowledge relevant to the lesson in terms of geography, math, science, and spatial skills. Paired-samples t-tests were conducted to determine significant differences in student performance. These t-tests indicate statistically significant improvements in all but one instance across all subjects, at all schools for both boys and girls. No statistically significant results were observed for a control group of an additional twenty-seven fifth graders. These results demonstrate the value of combining geography with math and science to improve student performance in STEM knowledge.

The most commonly used Finnish mathematics teacher guides (Grades 1-6) are investigated so as to determine what kind of resource they constitute for teachers in planning and enacting mathematics teaching and what kind of mathematics classroom they promote. The structure and the main contents of the guides were found to be quite homogeneous. The nature of communication was mostly descriptive, but the separate activities suggested for each lesson were quite explicitly described. Suggested activities, such as mental calculation tasks and homework assignment, were typically motivated by non-specific rationales, and many activities seemed to be taken for granted in the Finnish mathematics classroom culture. The results add both to knowledge about how to analyse teacher guides and to knowledge about Finnish educational features.

Validity evidence based on content is critical for making inferences about examinees’ responses to test items. Traditionally, content validity has been established by specifying the content domain ...

This qualitative study examines the challenges and supports inherent in a student-centered mathematics curriculum developed for a constructivist environment. Mathematics education faculty a...

Undergraduate research has become the centerpiece of many institutions of higher education’s efforts to attract and recruit high school graduates. Since 1987, throughout my tenure at Bloomsburg Uni...

Dr RL Moore was undoubtedly one of the finest mathematics teachers ever. He developed a unique teaching method designed to teach his students to think like mathematicians. His method was not designed to convey any particular mathematical knowledge. Instead, it was designed to teach his students to think. Today, his method has been modified to focus on using student participation toward the goal of the conveyance of mathematical knowledge rather than on Dr Moore's goal of teaching students to think. This article proposes that undergraduates would be better served if they took at least one course using Dr Moore's original method and his original goal.

There is a dearth of research on Tier 1 instruction designed to improve the mathematics achievement of English learners. This study examined the impact of a core kindergarten mathematics curriculum on the mathematics achievement of Spanish-speaking English learners (SS-ELs). Secondary aims tested for differential response to the curriculum among SS-ELs as a function of (a) mathematics skills at the beginning of kindergarten, (b) the number of SS-ELs in classrooms, and (c) the frequency of mathematical discourse during core mathematics instruction. Data analyzed in the study were generated from a recent large-scale efficacy trial. Participants were 556 SS-ELs from 66 kindergarten classrooms. Results suggest SS-ELs in treatment classrooms made greater gains than SS-ELs in comparison classrooms on mathematics measures across the school year. Evidence of differential response to the curriculum among SS-ELs was not found. The importance of core mathematics instruction and implications for school psych...

Quebec students have generally excelled in international mathematics comparisons and 22% performed in the top category, Level 6, on PISA in 2012. Several countries with more extensive gifted progra...