Search Results (13)

Exploring learning trajectories based on student thinking is needed to develop the teaching curricula, practices and educational support materials in mathematics for students with visual impairments. Hence, this study aims to reveal student thinking through various instructional tasks and tactile materials to explore the sequence of goals in the learning trajectory. A teaching experiment involving introductory information on algebraic and visual representations regarding advanced mathematical concepts was designed for correspondence and relations. The research was carried out with a braille-literate 10th-grade high school student with a congenital visual impairment where colour and light are not perceived in Türkiye. As a result of the teaching experiment, the participant was able to determine the correspondence and relations between two sets using different representations. He even designed graphic representations using the needle page. The learning trajectory goals and instructional tasks can serve as guides for research on curriculum development, practice design and material development. Full article

This paper presents research on the origin, scope, evolution, and rationale of knowledge about polynomials in high school mathematics. Within the framework of the Anthropological Theory of the Didactic, Croatian high school curricula and textbooks were analyzed, and four models of knowledge to be taught were identified in the period following the formal abandonment of New Math principles. None of the identified models provides a unified discourse that integrates knowledge about polynomials transposed from scholarly domains of algebra and mathematical analysis. In relation to other curricular content the knowledge about polynomials has two-fold importance: (1) contributing to the development of various techniques related to high school algebra and calculus; (2) serving as a fundamental example in the formation of the notion of a function. Thus, the observed reduction in polynomial content over the analyzed period affects both practical and theoretical knowledge. The findings suggest that curricular changes have primarily focused on the selection of knowledge, with scarce adaptations of knowledge to be taught compared to the knowledge before each curricular change. This has led to a persistent gap between algebraic and analytical approaches to polynomials, potentially influencing the learned knowledge even among the highest-achieving students. Despite polynomials’ epistemological and didactical potential to bridge high school algebra and calculus, their restriction to specific forms of algebraic expressions and linear and quadratic functions contributes more to the fragmentation of high school mathematics. Full article

Teaching computation in science courses can enhance science education, but doing so requires that teachers expand the vision of their discipline beyond the traditional view of science presented in most curricula. This article describes a design-based research (DBR) program that included collaboration among high school teachers and professional development leaders in physics and computer science education. Through three years of professional development and teacher-led development, field testing, and refinement of integrated curricular resources, we have combined instructional modeling practices, physical lab materials, and computer programming activities. One of the outcomes is a co-created framework for the integration of computational modeling into physics that is sensitive to teachers’ interests and expressed needs in addition to learning goals. This framework merges two evidence-based approaches to teaching: Bootstrap:Algebra, a web-based computing curriculum that emphasizes using multiple representations of functions and scaffolds that make the programming process explicit, and Modeling Instruction in physics, an approach that emphasizes the use of conceptual models, modeling practices and representational tools. In doing so, we uncover the need to balance teachers’ visions for integration opportunities with practical instructional needs and emphasize that frameworks for integration need to reflect teachers’ values and goals. Full article

Algebra as a school subject is ill defined. Students experience algebra quite differently depending on the perspective of algebra taken by authors of the textbooks from which they learn. Through a content analysis of problems (n = 63,174) in the narrative and homework sections of six high school mathematics textbook series published in the U.S., we acquired systematic and reliable information about the algebra strand (i.e., symbolic algebra and functions) of each textbook series. We introduce plots to show the density, distribution, and sequencing of content, and present analyses of data for cognitive behavior, real-world context, technology, and manipulatives. Feedback on this study from an author of each textbook series is shared, and findings are discussed in terms of students’ opportunities to learn. Full article

Performance in math, particularly algebra, is a major barrier to student success and participation in STEM among under-represented minoritized students, particularly Black U.S. high school students. This research applies social cognitive career theory (SCCT) to measure the impacts of an afterschool algebra for engineering program on math self-efficacy and interest in STEM among high school students in a large urban district. To study the program’s effects, a mixed methods research design was used where schools were assigned to either treatment or control conditions. Students in treatment schools accessed algebra for engineering modules, STEM professional role model videos, and field trips, while students in control schools accessed role model videos and field trips only. Surveys measuring math self-efficacy and STEM interest, outcome expectations, and choice goals were completed by participants in both conditions at the beginning and end of two separate program years, 2021–2022 and 2022–2023. Across both years, quantitative results suggest some positive effects of participation, particularly for STEM choice goals, but benefits depend upon student participation levels. Qualitative data offer student voice around prior experiences in math and science and the development of postsecondary plans in STEM. In combination, the results suggest that for students who do not initially identify as STEM career-bound, afterschool programming may not necessarily promote preparation for STEM careers due to an accumulation of weak math and science school experiences and other socio-environmental influences. Full article

The purpose of this study was to determine the predictiveness of community and family demographic variables related to the development of student academic background knowledge on the percentage of students who pass a state-mandated, commercially prepared, standardized Algebra 1 test in the state of New Jersey, USA. This explanatory, cross-sectional study utilized quantitative methods through hierarchical regression analysis. The results suggest that family demographic variables found in the United States Census data related to the development of student academic background knowledge predicted 75 percent of schools in which students achieved a passing score on a state standardized high school assessment of Algebra 1. We can conclude that construct-irrelevant variance, influenced in part by student background knowledge, can be used to predict standardized test results. The results call into question the use of standardized tests as tools for policy makers and educational leaders to accurately judge student learning or school quality. Full article

Mathematical manipulatives and the concrete–representational–abstract (CRA) instructional approach are common in elementary classrooms, but their use declines significantly by high school. This paper describes a mixed methods study focused on knowledge retention and perceptions of students in a high school Algebra I inclusion class after a lesson on square roots using a novel algebra manipulative. Twenty-five students in a high school Algebra I inclusion class engaged in an interactive lesson on square roots paired with the manipulative to support their conceptual understanding. Participants completed a pretest, a post-treatment questionnaire, and a delayed post-test. The two-sample t test showed a significant difference in students’ pretest–post-test scores. However, conventional content analysis of the questionnaires showed that most students did not believe the CRA instructional approach supported their learning. Implications include increased use of manipulatives to teach abstract algebraic topics to support students’ conceptual understanding and destigmatizing the use of manipulatives in secondary mathematics classrooms. Full article

This study involved 643 high school students to assess their performance in using different representations of linear functions—graphs, tables, and algebraic relationships—in mathematics and kinematics. The results show that students encounter greater difficulties when they have to interpret representations involving algebraic relations in mathematics. Furthermore, it is shown how the ability to switch from one type of representation to another is influenced by spatial reasoning skills, orientation toward physics, and self-confidence in the field of mathematics and physics. Implications for teaching kinematics and linear functions are briefly discussed. Full article

In this article, we propose an educational path to learn mathematics in the framework of the European Community Action Scheme for the Mobility of University Students (ERASMUS) project developed in an Italian high school class on the topic of the contribution of women in science. The choice of the educational path fell on Maria Gaetana Agnesi and the particular curve, the “versiera” (witch), studied by her. During the experimentation, the students have been divided into four groups, each one taking care of particular aspects of the human and cultural experience of Maria Gaetana Agnesi, and the construction of her famous curve under different mathematical registers: the geometric, algebraic, analytical, mechanical and computer science, as well as non-mathematical ones such as the gestural and voice registers. The effectiveness of the proposed educational path was evaluated through interviews with the students during the course and at the end of the activities. All the students, even those less skilled in mathematics, have shown enthusiasm and satisfaction by recognizing the mathematical object, the “witch”, presented by using different languages. Full article

The Victorian Curriculum and Assessment Authority (VCAA) introduced the use of Computer Algebra System (CAS) technology (calculator and software) into the senior secondary mathematics curriculum and examination assessment in three phases, starting with a research-based pilot from 2000, followed by parallel implementation of CAS and non-CAS subjects from 2006 and culminating in transition to CAS-assumed subjects in 2010. This paper reports reflections on these developments over two decades from the perspectives of a researcher and the state mathematics manager (the authors) in consultation with four implementing teachers (the consultants). The authors critically examined the strategic design decisions that were made for the initiative over time. Then, with contributions from the four consultants, technical design issues relating to assessment and to teaching and the changes over a decade were investigated. A range of modifications have been made over the two decades, driven by changes in device capability and progressively increasing teaching expertise. The place of CAS in senior mathematics is now widely accepted, partly because an examination component not allowing any technology has been implemented. Examination questions have become more general, which may have added difficulty, but more questions involve setting up a real situation mathematically. Full article

A usability study evaluated the ease with which users interacted with an author-designed modeling and simulation program called STEPP (Scaffolded Training Environment for Physics Programming). STEPP is a series of educational modules for introductory algebra-based physics classes that allow students to model the motion of an object using Finite State Machines (FSMs). STEPP was designed to teach students to decompose physical systems into a few key variables such as time, position, and velocity and then encourages them to use these variables to define states (such as running a marathon) and transitions between these states (such as crossing the finish line). We report the results of a usability study on high school physics teachers that was part of a summer training institute. To examine this, 8 high school physics teachers (6 women, 2 men) were taught how to use our simulation software. Data from qualitative and quantitative measures revealed that our tool generally exceeded teacher’s expectations across questions assessing: (1) User Experience, (2) STEM-C Relevance, and (3) Classroom Applicability. Implications of this research for STEM education and the use of modeling and simulation to enhance sustainability in learning will be discussed. Full article

Teaching and learning QM at high school as well as the undergraduate level is a highly non-trivial task. Indeed, major changes are required in understanding the new physical reality, and students have to deal with counterintuitive concepts such as uncertainty and entanglement as well as advanced mathematical tools. In order to overcome these critical issues, a simple approach is presented here, which is based solely on two-vector and 2 × 2 matrix algebra. Furthermore, it could also enable educational institutions to fill the gap between high school curricula and the current scientific and technological advances in physics by allowing students to gain some insight into topics such as qubits and quantum computers. The inspiration behind our proposal as well as its firm theoretical foundation are based on the famous Umdeutung (reinterpretation) paper by W. Heisenberg, which introduces QM in matrix form. Full article

This article continues to challenge the robust myth that mathematical smartness is exemplified in individuals who consistently complete mathematics problems quickly and accurately. In so doing, I present a set of counterstories from three students in one ninth-grade Algebra 1 classroom. These students described transformative experiences in their perceptions of mathematical smartness. Analysis of interviews revealed four themes about their perceptions of mathematical smartness, including: (1) consistently and unapologetically affording time and space to value multiple solution strategies, (2) belief in mathematical justification and explanation as the goal for demonstrating mastery of mathematical content, (3) valuing mathematically valid ideas from all class members, and (4) valuing collaborative problem solving as a way to help group members, distribute mathematical knowledge and orient students toward learning with one another. I found that their interpretations of mathematical smartness are counter to the still-dominant myths around speed and accuracy. While the four themes that emerged have been previously studied in the frame of teacher practices, this research provides needed additional empirical evidence of students’ voices describing what mathematical smartness can and should look like. Full article