General Education Mathematics Research Articles

Puzzles as a Didactic Tool for Development of Mathematical Abilities of Junior Schoolchildren in Basic and Additional Mathematical Education

Pedagogical science has always faced the issue of finding effective means for achieving educational results. This problem is especially urgent today, when in the rapidly changing world the tools, which yesterday could be used to support the interest of schoolchildren in study of mathematics and could provide an opportunity for the development of their mathematical abilities, quickly become obsolete. Today it is very important to search for new means that foster the development of students with the help of mathematics and mechanisms for including mathematics in the educational process. Thus, the aim of the article is to analyze puzzles as a didactic tool and study the possibilities of using puzzles in the process of teaching junior schoolchildren mathematics, both in the classroom and extra-curricular activities. The leading method here is the modeling of the methodical training system in general and additional mathematical education of schoolchildren, with the inclusion of a new didactic tool that fosters the students’ interest to the subject, develops individual mathematical abilities: logical thinking, abstraction, combining, operating spatial images, critical thinking, mathematical memory, etc. As a result of the research, the authors have determined the place, features and methodological aspects of the inclusion of puzzles in the process of teaching mathematics in general and additional school education. They can be used in the system of classical and creative math lessons and in extra-curricular activities of students: a mathematical club, a system of mathematical competitions, a mathematical camp, etc. The practical use of this model makes it possible to reduce the lack of tools in teaching for the development of students’ mathematical abilities, which in its turn, makes it possible to speak of purposefully high results in students’ mathematical activities, which is confirmed by the conducted experimental research.

Mathematics identities of competence in a middle-grades d/Deaf and hard-of-hearing classroom

ABSTRACTResearch in mathematics education among d/Deaf and hard-of-hearing (DHH) students has documented that DHH students lag behind their hearing peers on measures of mathematics achievement. The discrepancy is attributed to multiple factors, including mathematics instruction that focuses on skill and computation. Research focused on mathematics identity has great potential for advancing understanding of mathematics teaching and learning among DHH students by providing insight as to how current curricula, activities, and instruction do and/or do not benefit the learners. In this study, I examined the mathematics learning experiences of a group of DHH middle-grade students in a self-contained classroom. I drew upon theories of mathematics identity to examine what it means to do mathematics and to be a competent mathematics learner in this classroom. The general and mathematical obligations that emerged involved expectations of behaviors and proficiencies in the context of low-level mathematics activities. The characterizations of competence were based, in part, on jointly constructed expectations in the classroom. I present case-study analyses of two students, Anna and Vivian, to illustrate how the obligations and characterizations of competence, coupled with the students’ mathematics experiences and perceptions of d/Deafness, shaped how these students saw themselves and were seen by others as learners and as doers of mathematics. Anna’s experiences in the self-contained DHH mathematics classroom contributed to her beliefs that DHH individuals can be, and are, successful in mathematics. Vivian’s experiences mainstreamed in the general education mathematics classroom contributed to her beliefs that she and all DHH learners are less competent in mathematics, compared to hearing learners. Several new and related questions emerged with implications for practice and further research.

Investigating College Students' Reasoning With Messages of Risk and Causation

ABSTRACT Language of risk and causation pervades modern media sources. In response, statistical literacy is often framed as a critical means of understanding such discourse. At Michigan State University, several faculties have worked to create a new mathematics course, entitled Quantitative Literacy, to fulfill the University's general education mathematics requirement. Though the course does not center exclusively on statistical thinking and methods, the curriculum does include attention to science reports in the media, among other topics, which are often based on research using statistical methods. In an effort to begin to understand how students reason with such articles before having taken the course, students in Quantitative Literacy answered several open-ended questions at the beginning of the semester in response to an opinionated news article about risk in relation to processed meats. Analysis of 152 students' responses using Toulmin's framework for argumentation revealed that the majority of the students agreed with the author's misleading message. These results suggest that prior knowledge and preexisting biases serve as potential barriers to the types of reasoning fostered in the course, and thus that the Quantitative Literacy curriculum should specifically attend to students' preexisting beliefs about the real-world contexts encountered in the course.

Developing a Mathematics Module for Students with Intellectual Disability in Higher Education

Individuals with intellectual disability (ID) have largely been excluded from accessing all levels of education and participating in college life. Fortunately, academic institutions around the world are slowly beginning to examine how they can support equal citizenship of individuals with ID within their community. In Ireland, one university has recently accredited an innovative higher education programme for college students with intellectual disabilities. One of the emergent modules focuses on mathematics and recognises the importance of developing students’ numeracy skills in order to confidently navigate today’s society. Despite the increased emphasis on general mathematics education, the authors found there to be a dearth of research regarding the development of such a module for students with ID. This paper describes the design and development of the mathematics module and also details its piloting and evaluation with a cohort of students with ID who were enrolled in a higher education course in an Irish university.

Courses on the Beauty of Mathematics: Our Version of General Education Mathematics Courses

This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed “math beauty” courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to master mathematical proofs in the context of the field of study, is described briefly with details given for one.

Quantitative Literacy at Michigan State University, 3: Designing General Education Mathematics Courses

In this paper, we describe the process at Michigan State University whereby we have created two courses, Math 101 and 102, designed to foster numeracy and alleviate mathematics anxiety. The courses--which are not sequential--provide a means of satisfying the University's general education requirement without taking college algebra or calculus, among other options. They are context-driven and broken into modules such as "The World and Its People" and "Health and Risk." They have been highly successful thus far, with students providing positive feedback on their interest in the material and the utility they see of it in their daily lives. We include background on the courses' history, their current status, and present and future challenges, ending with suggestions for others as they attempt to implement quantitative literacy courses at their own institution.

Institutionalising Virtual Math Resources at an HBCU

This paper describes the work of a five-year grant project for the purpose of creating and institutionalising virtual mathematics resources (i.e., short video lessons) for general education mathematics courses at a Historically Black College/University (HBCU) in the US for the improvement of student learning. The project was successful in creating full series of lectures for courses into videos and making them accessible to all students of the university at all times. Some data illustrating the impact of these efforts on performance and students’ experiences is also presented and discussed. For each course, we compared the passing rates of students who watched the video lessons with those of students who did not watch the videos. Passing rates for students who watched the videos were consistently higher than for students who did not watch, and the majority of student feedback indicated videos were viewed as helpful.

Modifying a Research-Based Problem-Solving Intervention to Improve the Problem-Solving Performance of Fifth and Sixth Graders With and Without Learning Disabilities

The purpose of the present study was to test the efficacy of a modified cognitive strategy instructional intervention originally developed to improve the mathematical problem solving of middle and high school students with learning disabilities (LD). Fifth and sixth grade general education mathematics teachers and their students of varying ability (i.e., average-achieving [AA] students, low-achieving [LA] students, and students with LD) participated in the research study. Several features of the intervention were modified, including (a) explicitness of instruction, (b) emphasis on meta-cognition, (c) focus on problem-solving prerequisites, (d) extended duration of initial intervention, and (e) addition of visual supports. General education math teachers taught all instructional sessions to their inclusive classrooms. Curriculum-based measures (CBMs) of math problem solving were administered five times over the course of the year. A multilevel model (repeated measures nested within students and students nested within schools) was used to analyze student progress on CBMs. Though CBM scores in the intervention group were initially lower than that of the comparison group, intervention students improved significantly more in the first phase, with no differences in the second phase. Implications for instruction are discussed as well as directions for future research.

Attitudes and Experiences in Liberal Arts Mathematics

For many university students, the last formal experience in a mathematics classroom is a single semester “general education” mathematics class. Traditionally, students in this type of class often hold negative attitudes towards mathematics. Here I study a sample of students from this population (49 students at a large, urban, comprehensive public university enrolled in a “math for liberal arts majors” course) to research whether a positive experience in a freshman-level general education mathematics course correlates with a positive change in the students’ attitude towards mathematics in general. I also explore which specific aspects of such a course contribute most to a positive student experience. The survey results show that while a positive experience in a freshman-level general education mathematics course correlates with positive responses in a student’s attitude about several key variable components of attitude (including motivation to do mathematics, perceived usefulness of mathematics, and confidence while doing mathematics), it does not correlate with positive change. The course aspects that most correlate with a positive experience include the teacher/professor, difficulty level of the course, and workload.

Analysing the use of history of mathematics through MKT†

In this article, we analyse three ‘classical’ cases of using history of mathematics in teacher training and reinterpret them using the framework of mathematical knowledge for teaching (MKT). We continue with a discussion of the potential benefits of applying MKT as a framework for discussion in research related to the use of history in mathematics education. MKT serves as an example of a framework from general mathematics education research which has something to offer in this respect. We argue that the MKT framework provides a powerful language to communicate results from research on the uses of history of mathematics to researchers in other areas of mathematics education research.

Integrating Universal Design and Response to Intervention in Methods Courses for General Education Mathematics Teachers

Traditionally, teacher education programs have placed little emphasis on preparing mathematics teachers to work with students who struggle in mathematics. Therefore, it is crucial that mathematics teacher educators explicitly prepare prospective teachers to instruct students who struggle with mathematics by providing strategies and practices that specifically address their needs. In this study, we describe the principles of Universal Design for Learning and Response to Intervention. More specifically, we discuss how one Mathematics Teacher Educator uses these frame works in her mathematics methods course to help prospective teachers become cognizant of early interventions and effective strategies that can be implemented to provide all students with the greatest opportunity to learn.

Writing to Enhance Understanding in General Education Mathematics Courses

We consider a variety of writing assignments used for two general education mathematics courses. The student writing ranges from brief informal pieces to more formal assignments that address the full scope of a course, with an emphasis on encouraging students to have a richer experience of mathematical people and ideas and of their own learning. The assignments incorporate multiple media, including novels and films, and are spread throughout a course so that students have frequent and regular exposure to writing.

Acoustics labs for a general education math and music course

This paper describes audio demonstrations and experiments that I use in my university level, general education mathematics course “Sounding Number: Music and Mathematics from Ancient to Modern Times.” These particular experiments illustrate frequency, timbre, pitch, beats, spectra, dissonance, tuning, and scale construction, which are a subset of the topics covered in the class. They can be performed with the free, open-source audio editor and recorder Audacity®.

Assessing the Effectiveness of the Redesigned Mathematics Program on Graduation and Retention Rates of Underprepared Students

Faced with directives from the Tennessee Board of Regents (TBR), which preceded more stringent directives noted in the Complete College Act enacted in 2010, Middle Tennessee State University (MTSU) was required to eliminate the Developmental Studies program in 2006. These instructions from higher levels focused on increasing the educational attainment of Tennessee’s citizens, while recognizing the decreased availability of state funding for higher education. The dictates also indicated that funding granted to higher education institutions should go beyond student enrollment to considering the numbers who are retained and graduate. On a local university level, the reality was many students satisfy overall admission criteria, but are underprepared in certain academic areas as denoted by American College Testing sub-scores. Faculty members were faced with complying with these directives while also being committed to meeting the needs of students who were admitted. MTSU was the first TBR school to implement a comprehensive redesigned program for underprepared students. Developmental mathematics courses were eliminated and prescribed sections, referred to as K-sections, of general education mathematics courses were developed. This article reports the results of an assessment of the redesigned program at MTSU on graduation and retention rates.

What Makes Mid-Tertiary Mathematics Multiple Choice Test Items Difficult: Task Numbers or Cognitive Levels?

The researchers ascertained the linear relationship between any two Multiple Choice Test (MCT) items’ facility indices (z), cognitive level (x) and “task numbers (y). A 50 itemed multiple choice test was administered on a random sample of 226 NCE students who offered a General Studies Education (GSE) mathematics course. The test has a reliability coefficient of 0.92. The sampled students’ responses were scored. The estimates of correlation coefficients: rzx = - 0.33, rzy = - 0.33 and rxy = 0.87 were obtained and found significant (p

Mathematics, Secondary Students With Disabilities, and Web 2.0 Technologies

The Internet and Web 2.0 technologies [i.e., (micro-)blogs, wikis, social networking sites, Voicethreads, etc.] allows today’s students to access mathematics and other general education curricula like never before. Since they already have the expertise in using the Internet, digital technologies, and other media compared to previous generations, it is imperative that teachers and students access these technologies to increase students’ understanding of and connections with the general education mathematics content. This article will discuss: (1) the mathematics performance of secondary students with disabilities; (2) technologies available for use in secondary mathematics classrooms; and (3) Web 2.0 tools that secondary students with disabilities can access and use in their mathematics classrooms and/or at home.

Randomized Evaluation of a Supplemental Grade-Wide Mathematics Intervention

A randomized controlled trial was used to evaluate the effects of a supplemental mathematics intervention that emphasized fluency building for computations and procedures. All fourth- and fifth-grade English-speaking students from a single school district who were participating in general education mathematics instruction and had a 2009 year-end accountability score were included in the study ( N = 537). Assignment to intervention or control conditions occurred at the classroom level with roughly half of classes being assigned to intervention and half being assigned to control conditions within each school. Outcome measures included the 2009 year-end statewide accountability measure in mathematics as well as three computation curriculum-based measurement probes of mathematics administered on three occasions during the school year. Implementation integrity data were collected in intervention classrooms via direct observation, teacher surveys, and monitoring of permanent products. Multilevel linear modeling (MLM) analysis was used to evaluate the effect of the intervention on student mathematics outcomes for all students and for students who were low performing at baseline. Intervention effects were detected at both grade levels (but not on all outcome measures). MLM was also used to evaluate the mediating effect of intervention implementation integrity on intervention effects. The integrity with which the intervention was implemented in intervention classrooms predicted end-of-year standardized measures of mathematics achievement and growth on curriculum-based measures. Implications for mathematics instruction in general and mathematics intervention within response to intervention models are discussed.

This Mattered to Me

A Survey of the Current Status of Visually Impaired Students in Secondary Mathematics, by Donald W. Rapp and Audrey J. Rapp, originally published in the February 1992 issue of the Journal of Visual Impairment & Blindness, Volume 86, pp. 115-117. When I was asked to take on this project and pick one single article that mattered to me, I found it to be very difficult. I have read The series editor of This Mattered to Me is Stuart H. Wittenstein, Ed.D., superintendent of the California School for the Blind. hundreds of articles from the Journal of Visual Impairment & Blindness (JVIB) that have had an impact on my professional career. Like many in the field of visual impairment, I have an array of professional teaching and research interests. Thus, picking just one article on one area of was quite difficult. After much thought, I decided to go back to my roots as an educator: secondary mathematics. My first job was at the Alabama School for the Blind as its secondary mathematics teacher, and it was during my time there that I began a never-ending search for any and all information related to teaching mathematics to students with visual impairments. During this search, I discovered the JVIB article, A Survey of the Current Status of Visually Impaired Students in Secondary Mathematics, by Donald W. Rapp and Audrey J. Rapp, which included the findings of a questionnaire that was answered by teachers of students with visual impairments. Timeless research When I first read the Rapp and Rapp article, it was already eight years old, but it was the only data that existed at that time that discussed the types of mathematics that were being taught to secondary students with visual impairments. The authors conducted a simple survey of teachers of students with visual impairments in six New England states. The survey included questions on which secondary mathematics courses the teachers' students were taking, how the students were aided in their general education mathematics courses, and what tools they utilized. The most profound aspect of the article was the finding that of the 40 students who were reported as using braille as their primary literacy medium, only 19 (over half) were not enrolled in typical secondary mathematics courses. From this finding, one can surmise that either a large proportion of the students studied had cognitive disabilities in addition to their visual impairment that inhibited their abilities to take secondary mathematics courses or that their IEP (Individualized Education Program) teams did not push them to enroll in higher mathematics courses. Although cognitive disabilities may have ruled out higher mathematics for a number of these students, I suspect the latter is true. In my experience in the field of visual impairment, unfortunately, I do not believe that conditions have improved since this article was published. Let this study serve as a reminder that students who are blind need to be encouraged to enroll in higher mathematics courses. The article also highlighted the need for increased teacher training in braille. I was moved by the fact that 73% of the teachers who responded to the survey expressed interest in a workshop to review concepts of algebra, geometry and algebra II, with application of the Nemeth Code (p. …

Academic music: music instruction to engage third-grade students in learning basic fraction concepts

This study examined the effects of an academic music intervention on conceptual understanding of music notation, fraction symbols, fraction size, and equivalency of third graders from a multicultural, mixed socio-economic public school setting. Students (N = 67) were assigned by class to their general education mathematics program or to receive academic music instruction two times/week, 45 min/session, for 6 weeks. Academic music students used their conceptual understanding of music and fraction concepts to inform their solutions to fraction computation problems. Linear regression and t tests revealed statistically significant differences between experimental and comparison students’ music and fraction concepts, and fraction computation at posttest with large effect sizes. Students who came to instruction with less fraction knowledge responded well to instruction and produced posttest scores similar to their higher achieving peers.

The problems of mathematics education at secondary schools and gymnasia

The article reviews the ties between secondary schools/gymnasia and universities, and also discusses complementary mathematics education. Major attention is directed to the general mathematics curricula of general education and secondary education. A proposal of developing an integral mathematics education curriculum for gymnasium as well as withdrawing the state school graduation curriculum (by organising the examination under the general mathematics education curriculum) has been put forward.