Meaningful Mathematics Research Articles

Teaching mathematics remotely: changed practices in distance education

This investigation explored the challenges of creating meaningful mathematics practices for a community engaged in Distance Education (DE). Specifically, the study maps the influence of new technologies on the practices of a learning community where mathematics was taught remotely. The theoretical framework of this study utilised Bourdieu’s work on practice to consider the changed nature of the field, in this case, remote education provision, over time. By using Bourdieu’s notion of field, we are better able to understand the ways in which practices and discourses shape particular ways of working in rural education provision. The results of the study show that Field 1 was innovative and beyond the non-school world, while Field 2 lagged behind the technological resources of the non-school world.

TRANSFORMASI BUDAYA MELALUI PEMBELAJARAN MATEMATIKA BERMAKNA DI SEKOLAH

Abstract: One of many other functions of teaching at school level is as a means of cultural transformational process. Mathematics, one of the sciences resulted from human thoughts and activities, at school level is now expected to be more meaningful through the insertion of familiar concepts which are related to the local culture of the students. This cultural incorporation is then extended into national culture with its multicultural characteristics and global culture which is commonly cross-cultural based. Through this, it is hoped that culture can be applied and kept by our young generation through their way of thinking, viewing and doing things. All these can also increase their commitment to keep the cultural differences nation wide. Keywords: Cultural transformation, meaningful mathematics teaching, local culture, multicultural, cross-cultural understanding.

Engaging Students in Meaningful Mathematics Learning: Different Perspectives, Complementary Goals

Engaging Students in Meaningful Mathematics Learning: Different Perspectives, Complementary Goals

Pen Pals: Practicing Problem Solving

What is a good mathematics problem? What is a good mathematics problem for students at a particular grade level? How can I make mathematics interesting to students and fun? Preservice teachers explored these questions as they participated in a pen pal project with fifth and sixth graders. The teachers presented the middle schoolers with custom-made, meaningful mathematics problems. The students honed their communication skills and received personalized feedback about their learning. Along the way, many became more motivated by mathematics than they had been, and some, stimulated by the interaction with college students, began thinking about the future and college.

Sound Off!: Student Engagement and Teacher Guidance in Meaningful Mathematics: Enduring Principles

I learned to ride a bike at age six. The experiences leading to my first solo bike ride are still vivid memories. First, my father gave a wonderful explanation of bike riding. The mechanics of leg motion required to pedal were explained. Hand placement on the handlebars and the nuances of steering were described with clarity. Braking, maintaining balance, and every other conceivable aspect of bike riding were laid before me. Next, my brother modeled bike riding. Down the block he rode: peddling, steering, maintaining balance. He managed a 180-degree turn, returned, braked, and came to a perfect stop. Having gained a conceptual understanding of bike riding and having observed successful bike riding, I was able to ride the bike by myself at first attempt. I attribute my riding independence to my father's excellent explanation and my brother's superb modeling.

Exploring Segment Lengths on the Geoboard

Given a 5-peg × 5-peg geoboard, how many different lengths can be made by stretching a rubber band to form an oblique (nonhorizontal, nonvertical) segment between any two pegs? This question launches an investigation that requires students to make connections to the Pythagorean theorem, congruence, and combinations. It also leads to the question, “Can the results be generalized to an n-peg × n-peg geoboard?” (Note that we use “n-peg × n-peg” to refer to the dimensions of the geoboard to prevent confusion with the length of the side of the geoboard, which would be n − 1.) With its use of visual representation and potential mathematical ideas that can be explored from simple to complex, this task makes meaningful mathematics accessible to learners with varied levels of prior knowledge. In addition, mathematics vocabulary such as oblique and congruent are introduced in a meaningful context, making the lesson ideal for developing academic language.

Card Sorts, State Tests, and Meaningful Mathematics

“Data-driven decision making” is a phrase that is now commonplace in educational conversations. It is used when school districts discuss strategies to help meet the needs of all students while closing the achievement gap between subgroups of students. Within mathematics education, there is a growing need to educate prospective and practicing mathematics teachers about No Child Left Behind accountability measures and corresponding data within a given state in a way that emphasizes meaningful mathematics instruction that is consistent with national recommendations (NCTM 2000). Given pressures that teachers face within high-stakes teaching environments, it is important to analyze assessment tools, such as state-mandated tests, in an efficient, enlightened manner. A goal of such an analysis is to acknowledge accountability through constructive discourse while continuing to emphasize good mathematics teaching. Such discourse about accountability can take on many forms (Chauvot 2006). This article shares card-sorting activities that use items from state-mandated tests with prospective and practicing mathematics teachers. These activities give teachers tools to further accountability measures while exploring reformminded mathematics instruction.

고등학교 수학 수업에서의 죽음교육

The existentialist philosophers suggest death education because we can live better by recognizing our death. When we accept death as a part of our life rather than taboo and deny it, our life will be more important and abundant. The purpose of this study is to introduce death education to mathematics education. Now that school play roles of society and home, it should take responsibility for death education as well. Considering the cognitive aspect of death education using mathematical thinking, death education can be applied to mathematics class. Therefore this thesis proposes a plan to introduce death education into highschool mathematics class and seeks a practical teaching method. Introducing death education to mathematics class, we expect the meaningful mathematics class, the elevation of mathematics

The language policy practice in mathematics education in the upper west region of Ghana

Using Teacher's Assessment of Language Policy Practices (TAL2P) questionnaire and unstructured interview schedules, 63 randomly selected teachers (39 females, 24 males) from 21 schools within the Lawra District of the Upper West Region of Ghana were examined to determine the extent to which the language policy was practised. The study showed that teachers teach between 30-46% of their mathematics lesson periods in English at the lower primary level. Efforts to use the native language for meaningful mathematics instructions are constrained by teachers' inability to speak the language and the lack of materials in the native language. For children to derive the benefits of the language policy, the study recommends taking teachers linguistic competence into consideration during teacher postings and an urgent provision of text materials in the native languages to serve as resource materials for teachers. African Journal of Educational Studies in Mathematics and Sciences Vol. 2(1) 2004: 27-38

Facilitating Students’ Problem Solving in a Technological Context: Prospective Teachers’ Learning Trajectory

In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted and developed in their role of facilitating students’ mathematical problem solving with a technology tool. A cycle of planning–experience–reflection was repeated twice during an undergraduate course to allow the prospective teachers to change their strategies when working with two different groups of students. Case study methods were used to identify and analyze critical events that occurred throughout the different phases of the study and how these events may have influenced the prospective teachers’ work with students. Looking across the cases, several themes emerged. The prospective teachers (1) used their problem solving approaches to influence their pedagogical decisions; (2) desired to ask questions that would guide students in their solution strategies; (3) recognized their own struggle in facilitating students’ problem solving and focused on improving their interactions with students; (4) assumed the role of an explainer for some portion of their work with students; (5) used technological representations to promote students’ mathematical thinking or focus their attention; and (6) used the technology tools in ways consistent with the nature of their interactions and perceived role with students. The implications inform the development of an expanded learning trajectory for what we might expect as prospective teachers develop an understanding of how to teach mathematics in technology-rich environments.

The extent to which mathematics instructional practices in early childhood education in Zimbabwe relate to or make use of children's experiences

The aim of the study was to establish the extent to which mathematics instructional practices in early childhood education relate to or make use of children's experiences. The major question that guided the study was: In which ways do early childhood teachers use children's out-of-school strategies and everyday experiences in teaching mathematics? The study was conceptualised within a constructivist framework, in which meaningful mathematics instruction for young learners capitalises on their prior knowledge and the ways they solve their daily mathematical problems, and promotes active thinking in the process of making meaning. The study was qualitative, involving classroom observations using videotapes, interviews with teachers and questionnaires with Grade 1 and 2 teachers in a district of Masvingo, Zimbabwe. The major findings of the study were: teachers used children's knowledge minimally when introducing lessons and failed to build on children's knowledge throughout the lessons. There were observably low motivation and low performance by children during lessons. The ramifications of the study for policy and practice are discussed.

The Thirteen Days of Halloween: Using Children's Literature to Differentiate Instruction in the Mathematics Classroom

How children's literature can be used to provide meaningful mathematics instruction for children functioning at a variety of instructional levels in a single classroom. Teachers can use this information to select appropriate children's literature to use in their classroom to meet the needs of a diverse group of learners.

More Meaning From the Geometric Mean

We are all familiar with the average, or arithmetic mean, of two numbers. Less frequently used is the notion of the geometric mean. In “Geometric Meaning in the Geometric Mean Means More Meaningful Mathematics” in the March 2001 issue of the Mathematics Teacher, Matt E. Fluster shows how the geometric mean, s = _ab, of two positive numbers, a and b, can be used in a first-year algebra course to tie together geometric, algebraic, and computational investigations. In this article, I add a bit of history and an example suitable for more advanced courses. The example uses the geometric mean to compute square roots with Newton's method and does not require calculus. The history surrounding these concepts provides an opportunity to point out the universal nature of mathematics as a human activity. The basic ideas in this article were alive in the minds of ancient peoples who lived in what are now India, Pakistan, Iraq, and Egypt.

What Counts and How: Mathematics Teaching in Culturally, Linguistically, and Socioeconomically Diverse Urban Settings

This article presents findings from an ongoing study of urban teachers' efforts to embrace mathematics reform with student populations that are culturally, linguistically, and socioeconomically diverse (CLSD). We investigate the teacher's role in providing accessible and valuable mathematical learning opportunities to diverse students. Through narrative vignettes of practice and analyses of the personal and intellectual resources teachers draw on in CLSD contexts, we examine the challenges and possibilities two third-grade teachers face as they attempt such reform. One teacher's strengths were in making cultural connections with her students; the other's strengths were in pursuing complex and meaningful mathematics with her students. Building on our analysis, we offer a framework for examining the work of attending to mathematical and cultural issues simultaneously. Our findings suggest that such work is complex; however, teachers are seldom supported in their efforts to integrate these two perspectives. Our aim is to examine the dimensions of culturally relevant mathematics teaching and explore where the fields of mathematics and bilingual-bicultural education need to speak to one another.

Choosing Problems with Entry Points for All Students

Teachers frequently ask, “How can I teach everyone in my classroom when the mathematical knowledge and ability levels are so varied? Is it possible to teach meaningful mathematics without dividing the students into separate ability-level groups?” To solve this dilemma, I look for problems that can be explored on several levels.

The Line Between Comedy and Meaningful Mathematics

The Line Between Comedy and Meaningful Mathematics

Prospective Elementary Teachers' Mathematics Subject Matter Knowledge: The Real Number System

As the nation's educators attempt to prepare children who can be productive adults in a quantitative, technological, and global society, much emphasis is placed on children's learning and success in mathematics. In turn, the mathematics subject matter knowledge of the teachers who facilitate learning experiences for children is an important component of the research and practice agenda in mathematics education. This article focuses on the prospective elementary teachers' mathematics subject matter knowledge in relation to the real number system. The results from an open-ended assessment completed by 93 prospective elementary teachers indicated that the participants' understanding of the real number system (specifically integers, natural (counting) numbers, rational numbers, and whole numbers) was deficient. Based on this finding the author challenges teacher educators to focus on the mathematics preparation and meaningful mathematics experiences of prospective elementary teachers

Ethnomathematics in Teacher Education

This paper describes the need and rationale for a culture-inclusive course for prospective and practicing mathematics teachers. From the principles used in such a course as it was originally taught in 1993, up to the present, the graduate ethnomathematics course stresses as a key element students' ownership of their individual and personally meaningful cultural mathematics projects. The projects, personally chosen by students, are reported in the course in writing and in verbal presentations to the class together with activities suitable for school students. Related research which was carried out in a high school mathematics class is also described, together with some of the issues and constraints which arose. Finally, after a description of the course, two examples of students' projects are provided.

Upgrading High School Mathematics Instruction: Improving Learning Opportunities for Low-Achieving, Low-Income Youth

Low-achieving, low-income students are typically tracked into dead-end math courses in high school. In this article, the authors evaluate the success of “transition” math courses in California and New York, which are designed to bridge the gap between elementary and college-preparatory mathematics and to provide access to more challenging and meaningful mathematics for students who enter high school with poor skills. The authors hypothesize that the transition courses—Math A in California and Stretch Regents and UCSMP Math in New York—allow students to keep pace with those who enter college-preparatory courses by covering rigorous mathematical content using a range of cognitive strategies. Data from 882 students in 48 math classes are analyzed using a three-level hierarchical linear model. The results show that growth in student achievement is significantly lower in general-track classes than in college-preparatory classes. Achievement in transition classes falls in between: not significantly lower than in college-preparatory classes, but not significantly greater than in general-track classes. More rigorous content coverage accounts for much of the achievement advantage of college-preparatory classes. The transition classes are judged a partial success in meeting their goal of upgrading the quality of mathematics instruction for low-achieving, low-income youth.

A Credit-Union Project

I forgot my lunch money!” “I need a folder for math class today!” “Can I phone home and ask if I can stay after school to see the basketball game?” These types of authentic problems present opportunities to engage middle-grades students in meaningful mathematics. By establishing a classroom credit union, students can develop independence in solving real problems and model solutions used in the real world to solve similar problem. A classroom credit union also promotes the type of mathematics espoused in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) because it—engages students in authentic mathematics;promotes mathematical thinking, communication, and reasoning in solving problems;constitutes an ongoing mathematics activity;encourages students to verify solutions to problems;involves students with technology; andallows the teacher to be a facilitator of mathematics learning.