A COMPARATIVE STUDY OF QUADRILATERALS TOPIC CONTENT IN MATHEMATICS TEXTBOOKS BETWEEN MALAYSIA AND SOUTH KOREA

This study compares Malaysian and Korean geometry content in mathematics textbooks to help explain the differences that have been found consistently between the achievement levels of Malaysian and South Korean students in the Trends in International Mathematics and Science Study (TIMSS). Studies have shown that the use of textbooks can affect students’ mathematics achievements, especially in the field of geometry. Furthermore, to date, there has been no comparison of geometry content in Malaysian and Korean textbooks. Two textbooks used in the lower secondary education system in Malaysia and South Korea were referred. The topic of quadrilaterals was chosen for comparison, and the topic’s chapter in the South Korean textbook has been translated into English. The findings show four main aspects that distinguish how quadrilaterals are taught between the two countries. These aspects include the composition of quadrilaterals topics, the depth of concept exploration activities, the integration of deductive reasoning in the learning content and the difficulty level of mathematics problems given at the end of the chapter. In this regard, we recommend the Division of Curriculum Development of the Malaysian Ministry of Education reviews the geometry content of mathematics textbook used today to suit the curriculum proven to produce students who excel in international assessments

A comparative study of geometry curricula

In the United States, geometry has long been offered to high school students in the tenth grade. Attempts have been made in recent years to expand the role of geometry across grades Pre-K through twelve. However, based on the latest TIMSS results, although students in the United States made gains in most content areas, they still struggle with geometric concepts compared to their counterparts in other nations of the world, primarily those in certain Asian countries like Singapore and China. We argue that the structure of the curriculum and the instructional strategies used in these countries may lead to more progressive reform strategies for the United States curriculum. These strategies may provide the catalyst to push our students back to the head of the class when assessed locally, nationally, and internationally

Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science

Function Concept: Learning from History

The importance of functions in school mathematics has grown tremendously within the past century. Functions have progressed from being scantly represented in school mathematics to being a core mathematical topic. C.B. Boyer (1946) acknowledged “The development of the function concept has revolutionized mathematics in much the same way as did the nearly simultaneous rise of non-Euclidean geometry. It has transformed mathematics from a pure natural science- the queen of the sciences- into something vastly large. It has established mathematics as the basis of all rigorous thinking – the logic of all possible relations” (Markovits, Eylor, & Bruckheimer, 1986, p. 18). Historical speeches and documents, such as Klein’s 1893 Evanston Colloquium, Moore’s 1902 presidential address to the American Mathematical Society, The Reorganization of Mathematics in Secondary Education Report (1923), and The Report of Progressive Education and Joint Committee (1940), advocated that functions and “relational thinking” be a core concept in school mathematics. In fact, Felix Klein considered functions to be the “soul of mathematics”, and advocated that teachers teach functional concepts. Fortunately, the recommendations made decades ago pertaining to the importance of functions, and the needs to readily integrate the function concept into school mathematics by researchers were not ignored. The recommendations made regarding functions decades ago are evident in today’s curriculum standards. Standards for mathematics require students to be able to define functions, describe functions, identify functions, analyze functions, and recognize patterns in function (NCTM, 2000; Common Core State Standards 2010). Most notably, The Common Core State Standards (2010) has functions as one of five conceptual categories in high school mathematics. Considering the increased emphasis placed on functions in school mathematics within the past century, we sought to describe how the function concept was presented in secondary mathematics textbooks prior to the “New Math” era

Students\u27 Epistemological Beliefs of Mathematics When Taught Using Traditional Versus Reform Curricula in Rural Maine High Schools

This study compared students’ epistemological beliefs of mathematics after completing 3 years of a reform-oriented curriculum developed by the Core-Plus Mathematics Project (CPMP) versus a more traditional curriculum developed by Glencoe Mathematics. The Conceptions of Mathematics Inventory (CMI; Grouws, Howald, & Colangelo, 1996) was administered to 11th-grade students in four rural Maine high schools (n=102) to measure student beliefs of mathematics. CPMP was used as the primary textbook series in 2 of the schools, while the other 2 schools used Glencoe Mathematics. A variation of the Reformed Teaching Observation Protocol (RTOP; Piburn & Sawada, 2000) and teacher questionnaires were used to characterize the level of reform-oriented instruction occurring in each of the schools. The results indicated that the students who were taught using the traditional curriculum combined with reform-oriented teaching practices expressed the most positive beliefs of mathematics, while the students who were taught using the reform-oriented curriculum expressed less healthy beliefs of mathematics, especially when taught using reform-oriented teaching practices. Some of the differences in beliefs appeared to be gender-related. This study extends the previous research of Grouws et al. (1996), Walker (1999), and Star and Hoffmann (2005) by demonstrating the feasibility of using instruments such as the CMI to assess students’ epistemological beliefs of mathematics in order to expand the notion of impact of reform-oriented curricula beyond students’ performance on achievement tests. This study also illustrates the importance of determining what is actually happening in the classrooms when performing such research

Mathematics Anxiety in Society: A Real Phenomena and a Real Solution

While math anxiety still remains a real issue affecting student performance and confidence, today it is even more critical with the greater emphasis on producing more students for careers in STEM fields. In an effort to understand ways to ease math anxiety and encourage adaptive achievement behaviors to deal with such anxiety, this paper will explore the topic and provide research-based practices in providing a solution to this existing problem in our schools. There are many studies that show using technology in the teaching of mathematics will help to alleviate math anxiety and encourage students to enjoy learning mathematics. GeoGebra, a dynamic mathematics software, can assist in developing a deeper understanding of geometric/measurement/algebraic concepts in the mathematics classrooms from Grades K-16. Emphasis on addressing math anxiety as a teacher and using technologies like GeoGebra software to teach math are the main foci of the paper

Integrating Diversity Training into Doctoral Programs in Mathematics Education

There exists a need to promote diversity, equity, and inclusion in mathematics education (Wilson and Franke, 2008). Being cognizant that there are few underrepresented groups that obtain doctoral degrees in mathematical sciences or mathematics education (AMS, 2014; Reys and Dossey, 2008), focused training is needed to prepare doctoral students on diversity issues that may arise in higher education and the means by to address such issues. An advance seminar course or colloquium that would be helpful to mathematics education doctoral students who seek a career position in higher education should be entitled, “Gaining a better perspective of diversity in higher education”. This course would addresses issues related to establishing and sustaining an equitable and inclusive environment in classroom environments and throughout the university. “Climate can be examined through various components…structural diversity (the number of underrepresented students on a campus), the psychological climate (prejudice), and behavioral dimensions (relations among students, an instructors’ pedagogical approach)” (Hurtado, Milem, Clayton-Pedersen, and Allen, 1999, p. x). The climate is often enacted in the hidden curriculum that complements the overt curriculum of the university. Admittedly, diversity courses taught at many universities might address diversity climate issues, however it is not a requirement for a doctorate in mathematics education, and hence most doctoral students in mathematics education never enroll in such courses. Considering that by the year 2044, more than half of the U.S. population will be individuals of color (Colby & Ortman, 2015) and the academy is becoming increasingly diverse, it is imperative that we train educators to work within such diverse contexts. Thus, gaining an understanding of the complexities of diversity, and how to incorporate it into their practice will be vital to mathematics education doctoral students’ success in academia. Therefore, we propose that an advance seminar course or colloquium in mathematics education be dedicated to the teaching of diversity, equity, and inclusion in higher education: We will first discuss the content that should be covered, and subsequently describe how the training should be organized. By first shedding light on what ought to be learned, faculty members can strategically incorporate pedagogical strategies to promote the learning of the desired content

When Two Wrongs Made A Right: A Classroom Scenario of Critial Thinking as Problem Solving

Educators from kindergarten through college often stress the importance of teaching critical thinking within all academic content areas (Foundation for Critical Thinking, 2007, 2013). As indicated by the position statements of the National Council of Teachers of Mathematics, high quality mathematics education before the first grade should use curriculum and teaching practices that strengthen children’s problem-solving and reasoning processes as well as representing, communicating, and connecting mathematical ideas” The joint position statement of NAEYC and the National Council of” (NAEYC & NCTM [2002] 2010, 3). Through the educational and academic institutions critical thinking is identified as an important outcome for achieving the higher orders of learning upon successful completion of a course, a promotion, or a degree (Humphreys, 2013; Jenkins & Cutchens, 2011). Although there are numerous definitions of critical thinking, the authors have selected the definition by Scriven & Paul, 2008 as “the intellectually disciplined process of actively and skillfully conceptualizing, applying, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection reasoning, or communication as a guide to belief and action” (Scriven & Paul, 2008). Instructors should teach problem solving within the context of mathematics instruction and engage students in critical thinking by thoughtful questions with discussion of alternative results. Teaching preschool children to problem solve and engage in critical thinking in the context of mathematics instruction requires a series of thoughtful and informed decisions

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie