Traditional Mathematics Curriculum Research Articles

Unplugged activities in the elementary school mathematics classroom: The effects on students’ computational thinking and mathematical creativity

The rapid development of artificial intelligence technology has led to the proliferation of computational thinking (CT) education. However, research on unplugged activities’ influence in elementary math classrooms is limited, despite some exploring programming's cognitive benefits. This study presents both qualitative and quantitative analyzes stemming from a ten-week quasi-experimental research endeavor, specifically tailored for third-grade students. The research devised a series of unplugged activities, encompassing mathematical games, hands-on construction of mathematical logic boards, and calculating shopping discounts. The overarching objective was to investigate the impact of these unplugged activities on students’ mathematical creativity and CT. Students participating in a mathematics curriculum based on unplugged activities (N = 47) were compared with students participating in a traditional lecture-based mathematics curriculum (N = 46). The results indicated that unplugged activities exhibited significant advantages in fostering students’ CT and mathematical creativity across three dimensions, namely, problem-posing creativity (t = 5.830, p < 0.01), problem-solving creativity (t = 6.633, p < 0.01), and creative self-efficacy (t = 7.554, p < 0.01). Furthermore, the study revealed a relationship between students’ mathematical creativity as a predictor of CT. The results of the quantitative analysis were supported by the teacher's and students’ interview data, and the students felt excited and interested in the unplugged activities, whereas some students using the lecture-based method reported boredom and lack of interactivity. This research offered valuable insights for mathematics and CT education practice, underscoring unplugged activity as an innovative instructional approach that brings forth new possibilities for traditional mathematics teaching, with potential applications in the K-12 curriculum.

Postsecondary general education mathematics: theory and practice

Many students who take a mathematics course as part of their post-secondary education are not enrolled in a mathematically-intensive degree program. This poses a challenge to mathematics departments that, for example, value and privilege more traditional mathematics curriculum: should students in such courses be taught differently than those in more traditional mathematics courses? What should constitute the curricula of these courses and who should teach them? How might the local institutional context influence the courses that are ultimately offered? This paper sketches a theory intended to help frame responses to these questions. We then present an example of this theory in action, in the form of a general education mathematics course for first-year, underprepared students. The ongoing design, teaching, and evaluation of this course might inspire further revisions to general education in mathematics at the undergraduate level. We present the motivation for the design of the course, a summary of what was ultimately enacted, and our reflections of this ongoing event. Our intention here is not to present our course and an evaluation of its ‘success' – however that might be conceptualised – but rather to display a rigorous vision for post-secondary general education mathematics.

Enriching Undergraduate Mathematics Curriculum with Computer Science Courses

Traditional mathematics curriculum faces several issues nowadays. The gap between course materials and students’ real-life mathematical experiences, the scattering of knowledge in different courses, and the lack of mathematics applications to other subjects all hinder the learning of students. The emerg-ing trends in data science, machine learning, and artificial intelligence also impel higher education to enrich and refine mathematics education. In order to better incubate students for future, the experience of enriching undergrad-uate mathematics curriculum with computer science courses is introduced in this study. The curriculum is designed and implemented for students who major in applied mathematics to better stimulate the learning, participation, exercise, and innovation. It provides students with comprehensive theoretical and practical knowledge for the challenges and industrial requirements now-adays. Evaluations, major findings, and lessons learned from three refined courses are discussed for more insight into the following deployment and re-finement of the curriculum.

Preservice teachers learning to teach proof through classroom implementation: Successes and challenges

Proof and reasoning are central to learning mathematics with understanding. Yet proof is seen as challenging to teach and to learn. In a capstone course for preservice teachers, we developed instructional modules that guided prospective secondary mathematics teachers (PSTs) through a cycle of learning about the logical aspects of proof, then planning and implementing lessons in secondary classrooms that integrate these aspects with traditional mathematics curriculum in the United States. In this paper we highlight our framework on mathematical knowledge for teaching proof and focus on some of the logical aspects of proof that are seen as particularly challenging (four proof themes). We analyze 60 lesson plans, video recordings of a subset of 13 enacted lessons, and the PSTs’ self- reported data to shed light on how the PSTs planned and enacted lessons that integrate these proof themes. The results provide insights into successes and challenges the PSTs encountered in this process and illustrate potential pathways for preparing PSTs to enact reasoning and proof in secondary classrooms. We also highlight the design principles for supporting the development of PSTs’ mathematical knowledge for teaching proof.

Analysis of Pre-Service Teachers' Interpretation and Utilization of Non-Textual Elements in Mathematics Curriculum Materials

This study explores how pre-service teachers (PSTs) view, interpret, and utilize non-textual elements (NTEs) in mathematics curriculum. Fifty-two PSTs, who enrolled in a mathematics methods course at a Midwestern university in the U.S., engaged in a three-part task that consisted of evaluations and modifications of NTEs in the sample mathematics curriculum materials. We ascertain what PSTs consider to be the strengths and weaknesses of NTEs, how they define the primary goals of NTEs, and how they would work to modify or adapt existing NTEs with effective teaching in mind. By using the Curricular Noticing Framework, we can better understand how PSTs recognize opportunities within mathematics curriculum and gain a deeper understanding regarding how PSTs’ prior experiences may affect their curricular-attending habits, which has consequences for their future teaching. Findings indicate that PSTs understand NTEs to be simply a support for traditional mathematics curriculum, rather than tools on their own. Also, they tend to prefer NTEs that are familiar to them. From our findings, we draw implications for teacher educators who support PSTs’ interpretation and utilization of NTEs.

Story as a Mathematics Instructional Strategy

Traditional mathematics curriculum does not always meet the student’s needs. Lecturing students does not engage, motivate, and activate their critical thinking skills. Essentially, the curriculum has become separated from the real-world context in which mathematical theorems are applied. Students don’t understand the purpose in their learning. STEM curriculum focuses on the content areas of science, technology, engineering, and mathematics; however, the STEAM curriculum takes the STEM curriculum a step further by incorporating the arts into those content areas. By doing so, it reaches more students in an innovative approach of the creative process. The instructional strategy of story is the arts of STEAM curriculum. By incorporating story into mathematics curriculum, it is engaging and motivating students to learn the content from a student-centered approach. Students are become fully embraced within the story and use the mathematical content to apply and predict the story outcomes. It requires students to continuously reflect, communicate, and apply their mathematics ideas to the story.

The Effect of Constructivist Mathematics on Achievement in Rural Schools

International assessment data indicate American students are not competing with their counterparts in other countries. The mathematics curriculum and pedagogy are not preparing students to compete in a global economy. This study compared student achievement using sixth grade mathematics results from the Illinois Standards Achievement Test. Specifically, the study compared the results of students in three different rural school districts, all of whom were receiving instruction in three different mathematics curricula. In one district, students received seven years of the K-6 Everyday Mathematics curriculum which was compared with students who received seven years of instruction using a traditional mathematics curriculum in the second district and in the third district scores were compared with students who were taught using a traditional mathematics curriculum supplemented with Mountain Math. The results of this study indicate the constructivist K-6 elementary mathematics curriculum did not lead to higher levels in math achievement when compared with the traditional methods of instruction.

Why Literacy Should be Included in an Effective Elementary Math Curriculum

This article provides a brief overview of the key benefits of interdisciplinary instruction combining literacy and math, in addition to sharing three integrated lessons used in support of a traditional elementary mathematics curriculum to effectively review number bonds through 10 and simple additional and subtraction.

Evaluating online resources in terms of learning environment and student attitudes in middle-grade mathematics classes

The main objective of this research was to use learning environment and attitude scales in evaluating online resource materials for supporting a traditional mathematics curriculum. The sample consisted of 914 middle-school students in 49 classes. A second research focus was the validation of the chosen learning environment questionnaire, the Technology-Rich Outcomes-Focused Learning Environment Inventory (TROFLEI), with an ethnically-diverse sample of middle-grade mathematics students in Florida. Finally, we complemented quantitative questionnaire data with qualitative interview data that were analysed thematically. In addition to cross-validating the TROFLEI, our study suggested that the online resource provided neither much advantage nor much disadvantage.

Understanding Problem-Solving Errors by Students With Learning Disabilities in Standards-Based and Traditional Curricula

Students with learning disabilities struggle with word problems in mathematics classes. Understanding the type of errors students make when working through such mathematical problems can further describe student performance and highlight student difficulties. Through the use of error codes, researchers analyzed the type of errors made by 14 sixth grade and 15 seventh grade students with language-based learning disabilities educated with either a standards-based or traditional mathematics curricula on word problems representing number and operations and algebra standards. Two main findings occurred: (a) the open-ended word problems were challenging to students with learning disabilities as demonstrated through the high rate of unanswered questions and incorrect answers, with the most frequently committed errors representing a lack of understanding of the mathematics; and (b) no relationship existed between curricula and correct or unanswered questions for sixth grade, but statistically significant relationships existed in the seventh grade, favoring the standards-based curriculum.

Examining calculator use among students with and without disabilities educated with different mathematical curricula

This study assessed if students with and without disabilities used calculators (fourfunction, scientific, or graphing) to solve mathematics assessment problems and whether using calculators improved their performance. Participants were sixth and seventh-grade students educated with either National Science Foundation (NSF)-funded or traditional mathematics curriculum materials. Students solved multiple choice and open-ended problems based on items from the State’s released previous assessments. A linear mixed model was conducted for each grade to analyze the factors impacting students’ self-reported calculator use. Chi Square tests were also performed on both grade’s data to determine the relationship between using a calculator and correctly solving problems. Results suggested only time as a main factor impacting calculator use and students who self-reported using a calculator were more likely to answer questions correctly. The results have implications for practice given the controversy over calculator use by students both with and without disabilities.

Supporting Math Skills with Children's Stories

In the traditional mathematics curriculum, students are encouraged to memorize numbers and their operations as a means of building larger and larger fact-based assemblies of an increasingly complex...

Longitudinal investigation of the curricular effect: An analysis of student learning outcomes from the LieCal Project in the United States

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including students of color; (4) the use of CMP contributed to significantly higher problem-solving growth for all ethnic groups; and (5) a high level of conceptual emphasis in a classroom improved the students’ ability to represent problem situations. (However, the level of conceptual emphasis bears no relation to students’ problem solving or symbol manipulation skills.)

The teaching of equation solving: approaches in Standards-based and traditional curricula in the United States

This paper discusses the approaches to teaching linear equation solving that are embedded in a Standards-based mathematics curriculum (Connected Mathematics Program or CMP) and in a traditional mathematics curriculum (Glencoe Mathematics) in the United States. Overall, the CMP curriculum takes a functional approach to teaching equation solving, while Glencoe Mathematics takes a structural approach. The functional approach emphasizes the important ideas of change and variation in situations and contexts. It also emphasizes the representation of relationships between variables. The structural approach, on the other hand, requires students to work abstractly with symbols and follow procedures in a systematic way. The CMP curriculum may be regarded as a curriculum with a pedagogy that emphasizes predominantly the conceptual aspects of equation solving, while Glencoe Mathematics may be regarded as a curriculum with a pedagogy that emphasizes predominantly the procedural aspects of equation solving. The two curricula may serve as concrete examples of functional and structural approaches, respectively, to the teaching of algebra in general and equation solving in particular.

Middle-School Mathematics Curricula and Students with Learning Disabilities: Is One Curriculum Better?

Little is known about how best to teach mathematics to students with learning disabilities. This study explored the performance and self-reported calculator use of 13 sixth-grade and 15 seventh-grade students with learning disabilities educated in either standards-based or traditional mathematics curricula on multiple-choice and open-ended assessments. Across both groups of students: (a) curriculum did not impact the number of problems students answered correctly, (b) students answered more problems correctly on the multiple-choice than on the open-ended assessments, (c) students self-reported low percentages of calculator use, and (d) curriculum did not impact students' self-reported calculator use. Overall, the results suggest that students with learning disabilities are not advantaged or disadvantaged by receiving either a traditional or a standards-based mathematics curriculum.

Giving Exponential Functions a Fair Shake

In a traditional mathematics curriculum, middle school students' experiences with functions in algebra are usually limited to linear relationships. However, a number of realworld experiences (e.g., compound interest, population growth, and the amount of a drug remaining in a subject's bloodstream) involve exponential functions. In this article, I describe two problems involving exponential functions and some basic probability concepts that were used in an eighthgrade class, which led to greater student understanding about the general form of an exponential function. I also describe how students used graphing calculators to help them make sense of the values that are used in the general form and how they relate to the context of the problem.

Can We Reach Definitive Conclusions in Mathematics Education Research?

The reform mathematics curricula present students with problems that cannot be solved using routine methods. Ms. Latterell and Mr. Copes wonder about the best ways to teach students to solve such problems -- a research question that leads them into a classroom where a teacher is refereeing an animated discussion about algebra. WE ARE hearing a lot of noise these days about wars being waged over the content and pedagogy of new math curricula. These disagreements echo similar discussions in other fields: between whole language and phonics in reading, between prophetic versus priestly in the social sciences, between positivists and antipositivists in general. Can we ever decide which of these approaches is better? One way in which the so-called reform curricula in mathematics differ from the more traditional curricula is in their approach to teaching problem solving. Many who have taken mathematics courses remember solving lots of problems. is 3 + 2? Solve the equation 3x + 17 = 2 for x. The National Council of Teachers of Mathematics (NCTM), however, defines problem solving as engaging in a task for which the solution path is not routine.1 Problems in symbol manipulation can be solved by routine methods, and so would not constitute problem solving in the NCTM sense. Those notorious word problems, problems with practical applications, or puzzles more nearly match the NCTM criterion. There are no routine methods by which a student (or a computer) could solve these problems. Certainly, the traditional curricula do not eschew problem solving in the NCTM sense. Indeed, almost all curricula claim to be satisfying the new math standards as they are spelled out in Principles and Standards for School Mathematics. But the differences in how to teach problem solving are very real. What are those differences, and how should problem solving be taught? Let us begin to address these questions by considering one seventh-grade teacher's first-person description of an attempt to teach problem solving. Classroom Episode One I wrote the problem on a transparency as students were coming into the room, and I put it on the overhead projector as they got into their base groups and signed in. The problem was: Represent as an equation the claim that there are six times as many students as teachers in this school. Use S for the number of students and T for the number of teachers. I said, Please work on this for a few minutes in your groups. As I circulated, I found that all but one group had written 6S = T. Then I overheard Chris saying, Wait a minute -- if S was 100, then T would be 600, and that's not right. The group began to argue heatedly. I gave Chris a thumbs-up sign to keep the argument going and sent representatives from other groups to eavesdrop on the discussion. Soon the entire class was in turmoil. Different Approaches to Teaching Problem Solving Is using a problem that provokes controversy like this a good way to teach problem solving? Before we consider that question, let us look at the differences between reform-oriented and traditional approaches to teaching problem solving in mathematics. The restrictions of space demand that we oversimplify. Traditional mathematics curricula are based on the walk before you run philosophy. Until you know how to add 3 + 2, there is no way you can solve a problem such as You have 3 apples and are given 2 more; how many do you have? In these curricula, students learn the and then see how to apply them. That is, students must learn mathematics skills before they learn problem solving. Reform curricula, in contrast, are based on the idea that students retain basic mathematics best while trying to use them to solve engaging problems. Students who are set to work on interesting problems they do not know how to solve can be quite receptive to learning and problem-solving techniques on a need-to-know basis. …

FROM CALCULUS TO TOPOLOGY: TEACHING LECTURE-FREE SEMINAR COURSES AT ALL LEVELS OF THE UNDERGRADUATE MATHEMATICS CURRICULUM*

ABSTRACT The paper discusses the author's experiences teaching mathematics courses in a lecture-free, discussion-based seminar format at all levels of the traditional undergraduate mathematics curriculum. These seminars replace the traditional lecture with classroom discussion of course readings and exercises prepared by students in advance of class. Methods of motivating, instructing, and supporting student efforts towards independent reading of mathematical text is discussed. A non-scientific assessment of the results in these seminar courses is provided. The author's success with the seminar approach to mathematics education at all levels of the undergraduate curriculum suggests the potential value of subsequent experimentation in seminar instruction by other professors. Suggestions for such experimentation are provided. * This paper is an invited paper from the Contributed Paper Session on The Undergraduate Seminar in Mathematics at the New Orleans Joint AMS/AMA Mathematics Meetings, 10–13 January 2001.

Cubic Polynomials

A quadratic polynomial in two variables graphs as a conic section; conic sections are an important area of study in a traditional mathematics curriculum.

Some Characteristics of Eighth Grade Mathematics Classes in the TIMSS Videotape Study

situations involve only abstract concepts such as numbers and geometric shapes-even specific examples such as a rectangle three inches wide and five inches long-in contrast to concrete situations that involve physical or social representations of abstract concepts-such as a 3-by-5 inch index card. One reason reviewers were interested in this dichotomy was the call from some advocates of mathematics education reform in the United States for far more mathematics instruction to be done in real world contexts. Reviewers wanted to determine whether the proportion of concrete settings was significantly lower in the United States than in Japan or Germany. The locus of control of the solution of a problem-whether the task in the context of the class essentially included its own method of solution-is another aspect of the extent to which instruction was consistent with some current calls for reform of mathematics education in the United States. An important component of is the solver's control of the process of a [3]. A comparison of the extent to which exercises appear to require solvers to find solution methods should provide one indication of the extent to which mathematics instruction is oriented toward problem solving and also, perhaps, of the extent to which routine skills are emphasized. Similarly, the complexity of exercises is another indicator of their sophistication and mathematical richness, especially from a perspective. Determining whether a requires a single-step or multi-step solution depends upon not only the statement of the but also the presumed sophistication of the solver. For example, a simple linear equation such as 5x + 4 = 19 would be considered a two-step process for students who are first learning how to solve such equations but would constitute one very small step for students who had developed proficiency at systems of linear equations. As a result, reviewers had to consider the in the context of the class when judging its complexity. The reviewers classified the subject and described the subject matter of each class. Each of the 90 classes was classified according to its likely position in a traditional (1980s) United States college preparatory mathematics curriculum. The three classifications used were and Geometry. Approximately half the classes were classified as Geometry, 30% as Algebra, and the remainder as Before Algebra. The reviewers also rated each class on the basis of their judgment of its potential for helping students understand mathematics. The five categories used 1998] EIGHTH GRADE MATHEMATICS CLASSES 795 This content downloaded from 157.55.39.178 on Sun, 24 Jul 2016 06:17:36 UTC All use subject to http://about.jstor.org/terms were Weak, Almost Good, Better, and Strong. While this is quite subjective, the four reviewers were able to reach complete agreement in all 90 cases. Readers of this paper who would like to make their own judgments may send email to timss@ed.gov to inquire about obtaining copies of the tables and other data from the TIMSS video study. The table for each class consisted of a few pages, typically about three, that included a summary description of each segment of the class. Segments were defined and identified by the members of the Stigler laboratory. A new segment started when there was a significant change in activity or in the content being presented. Reviewers categorized each segment by the nature of its mathematical activity and by its role in the structure of the class. The segments became the nodes of the directed graphs used to represent graphically the structure of the