NCTM's Principles Research Articles

Augmented reality applications for mathematical creativity: a systematic review

AbstractAugmented reality (AR) applications are often studied in education. However, little literature has systematically reviewed the applications of AR for mathematical creativity. This paper aims to analyze the research trends comprehensively and systematically on 66 articles from 2015 to 2023. Based on the NCTM Principles and Standards guidelines, trends in the application of AR in mathematics education can be analyzed into six themes: equity, mathematics curriculum, mathematics teaching, learning, assessment, and mathematics technology. The results of the study show that (1) AR for mathematical creativity has implications for improving students' cognitive performance; problem-solving process; self-potential; social skills, and self-ability of students; (2) the most dominant features in developing AR applications for mathematical creativity are the Unity3D tool and Vuforia; (3) AR has a positive impact on equity for improving the quality of teaching and learning, supporting the educational curriculum; improve the teaching and learning of mathematics; effective evaluation and technology development in the learning process; (4) AR as a creative learning media; AR helps creative collaboration between students; and able to improve students' creative thinking skills. The results of a systematic review of AR applications for mathematical creativity can help educators and the development of future educational research.

Effective Teaching and Evaluation of Mathematics by Secondary School Mathematics Teachers in the North West Region of Cameroon

The study set out to examined the extent to which secondary school mathematics teachers implement the principles of effective teaching and evaluation of mathematics as put forward by the National Council of Teachers of Mathematics – NCTM; principles which when effectively implemented will enable learners to construct knowledge thereby doing away with mathematics phobia, and consequently performing better in mathematics. The study adopted a descriptive survey research design. The population of the study was made up of 600 public and private secondary school mathematics teachers serving in the North West Region of Cameroon. Using the Taro Yamane’s formula, 240 mathematics teachers selected through simple random sampling, constituted the sample of the study. Two research questions and two hypotheses guided the study. A questionnaire whose Cronbach alpha reliability was found to be 0.87 was used to collect relevant data. The data collected was analysed using mean to answer the research questions and t-test to test the hypotheses at the 0.05 level of significance. The findings of the study revealed that the level of implementation of the principles of effective teaching and evaluation of mathematics by secondary school mathematics teachers in the North West Region of Cameroon is significantly low. Furthermore, male and female mathematics teachers do not differ significantly in their implementation of the principles of effective teaching and evaluation of mathematics. It was recommended among other things that secondary school mathematics teachers should embrace the NCTM principles of effective teaching and evaluation of mathematics with finesse and incorporate them within their instructional programs and practices.

Evaluation of Primary School Mathematics Curricula of Northern and Southern Cyprus for NCTM Principles and Standards

Evaluation of Primary School Mathematics Curricula of Northern and Southern Cyprus for NCTM Principles and Standards

NCTM’s Principles and Standards for Developing Conceptual Understanding in Mathematics

The purpose of this study is to develop understanding of concepts in mathematics through the application of the NCTM's Principles and Standards. This research method is descriptive. The results obtained are understanding concepts in mathematics can be developed through the application of NCTM Principles and Standards consisting of 6 principles, namely: 1. Equity, 2. Curriculum, 3. Teaching, 4. Learning, 5. Assessment, and Technology. Understanding concepts in mathematics that can be developed are: a. defining concepts verbally and in writing, b. Make examples and not examples, c. Using various symbols to present a concept, d. Change the form of representation to various forms, e. Identifying the characteristics of a concept, f. compare various concepts, and g. interpret concepts.

Detecting and Reducing Bias in Questioning Patterns

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Investigating and mitigating implicit bias in questions are discussed in this article, which is another installment in the series.

Making Math Social

Teachers, students, and parents might wonder: Why should we make mathematics a social pursuit? Although individual study and reflection are important parts of any discipline, providing a culture of learning mathematics socially enhances sense making for students. According to NCTM's Principles to Actions: Ensuring Mathematical Success for All (2014), learning through discourse, activity, and interaction related to meaningful problems is a foundational principle for effective mathematics teaching.

Uncommon Partitions: Partitioning as a Problem-Solving Activity

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series.

Connecting the Dots: Building Procedural Fluency

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Student thinking, a learning cycle, and procedural fluency are discussed in this article, which is the second installment in the series.

Promoting a Conceptual Understanding of Mathematics

This article provides an overview of the eight effective mathematics teaching practices first described in NCTM's Principles to Actions: Ensuring Mathematical Success for All.

Two Instructional Moves to Promote Student Competence

Mrs. Hobbs's fourth graders are struggling. And it is working. This year, instead of teaching the state standard on unit conversion by showing students a procedure to follow, Hobbs asked her students to work in groups to develop a method. She is excited to promote more reasoning, problem solving, and use of varied solution pathways, in line with the NCTM's Principles to Actions: Ensuring Mathematical Success for All (2014). This is worthy work. But in some moments, for some students, the struggle does not feel productive. Several students are hesitant and lack confidence. A few give up easily. Hobbs does not want to go back to telling students a procedure, but she does not want to leave them to flounder.

Angle detectives

NCTM's Principles to Actions: Ensuring Mathematical Success for All outlines eight mathematics teaching practices for effective teaching and learning of mathematics (NCTM 2014, p. 10). The second practice, Implement tasks that promote reasoning and problem solving, involves effective teaching of mathematics that engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

Hundred Chart Challenge

NCTM's Principles to Actions:Ensuring Mathematical Success for All(2014) outlines eight teaching practices for effective teaching and learning of mathematics. One of them,Use and connect mathematical representations, involves engaging students in “making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving” (p. 10).

How Common Is the Common Core?

This article identifies major differences between NCTM's Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics, including examples and implications for practice.

Mathematics Teaching: Practices in Action

This call for manuscripts is requesting articles that provide evidence to support the Mathematics Teaching Practices found in NCTM's Principles to Actions: Ensuring Mathematical Success for All.

Call for Manuscripts: Mathematics Teaching Practices in Action

This call for manuscripts is requesting articles that provide evidence to support the Mathematics Teaching Practices found in NCTM's Principles to Actions: Ensuring Mathematical Success for All.

All hands on deck!

Math by the Month is a regular department of the journal, featuring collections of short activities focused on a monthly theme. These articles aim for an inquiry or problem-solving orientation that includes at least four activities each for grade bands K–2, 3–4, and 5–6. In the current issue, the problems are designed to actively engage your students in a literacy-rich mathematics environment, which is recommended by the NCTM Principles and Standards and the Common Core State Standards in Mathematics.

Proofs without Words: A Visual Application of Reasoning and Proof

Reasoning and Proof is one of the process standards set forth in NCTM's principles and standards for school mathematics (2000).

Connecting Geometry and Algebra in the Middle Grades

Welcome to the 2011 Focus Issue, which highlights connections between geometry and algebra that teachers can leverage in the middle grades. NCTM's Principles and Standards for School Mathematics (2000) recommends that students in the middle grades experience both the geometric representation of algebraic ideas and the algebraic representation of geometric ideas. By making these connections, students see that mathematical topics are related. They are not just a collection of isolated facts in seemingly disjoint fields but facts that often have many extensive connections.

NCTM Principles and Standards for Mathematically Talented Students

NCTM Principles and Standards for Mathematically Talented Students

Connecting Research to Teaching: Count on Number Theory to Inspire Proof

Many students find proofs frustrating, and teachers struggle with how to help students write proofs. In fact, it is well documented that most students who have studied proofs in high school geometry courses do not master them and do not understand their function (Battista 2007; Harel and Sowder 2007). And yet, according to NCTM's Principles and Standards for School Mathematics(2000), “By the end of secondary school, students should be able to understand and produce mathematical proofs … and should appreciate the value of such arguments” (p. 56).