Student Mathematical Thinking Research Articles

Improving Students' Mathematical Critical Thinking Abilities Through the Problem Solving Method on the Sequences and Series Course

This study aims to determine the improvement of students' mathematical critical thinking abilities through problem solving methods. This study was hold at MAN 3 Bireuen (High School Level) in the 2019/2020 school’s year. The research method was a quasi-experimental study design nonrandomized Pre-test Post-test Control Group Design. The population of the study were all students of Class XI MAN 3 Bireuen with purposive sampling technique. The study sample was to 30 students for the experimental class and 28 students for the control class. The skill increasing was calculated using normalized gain. Data were analyzed using the t test. The results showed that students’ critical thinking skills mathematically taught through problem solving methods is better than students mathematical critical thinking skills taught through conventional learning.

BERPIKIR KOMBINATORIK MATEMATIS SISWA DALAM MENGKONSTRUKSI KONSEP PELUANG

This qualitative research aims to describe activity of students mathematical combinatorial thinking in constructing of the opportunity concept. The subject of the study is two students of Junior High School who had the ability in constructing concept. Data collection was obtained at the time of learning carried out based on learning plan as research instruments. The results showed a combinatorial thinking activity in constructing concepts. Counting processes are showen by students identifying dice and coins, solving theoritical opportunities problems with tables or diagrams, and solving empirical opportunities problems. Formulas/exspressions are showen by students being able to construct sampel points and sample space, construct theoritical opportunities concept, and make mathematical formulas of opportunities. Set of outcomes is showen by students being able to find the results of solving theoritical opportunity problems of one/or more dice and coins as well as the results of solving empirically opportunity problems.Keywords: combinatorial thinking, constructing concept, opportunity

Clarifiable Ambiguity in Classroom Mathematics Discourse

ABSTRACTAmbiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking. We illustrate clarifiable ambiguity that occurs in mathematics classrooms and consider ramifications of not addressing it. We conclude the paper with a discussion about addressing clarifiable ambiguity through seeking focused clarification.

Teachers’ orientations toward using student mathematical thinking as a resource during whole-class discussion

Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during whole-class instruction. Teachers’ orientations—their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers’ use of student thinking as a resource is understanding their related orientations. To that end, the purpose of this study is to characterize teachers’ orientations toward using student mathematical thinking as a resource during whole-class instruction. We analyzed a collection of 173 thinking-as-a-resource orientations inferred from scenario-based interviews conducted with 13 teachers. The potential of each orientation to support the development of the practice of productively using student mathematical thinking was classified by considering each orientation’s relationship to three frameworks related to recognizing and leveraging high-potential instances of student mathematical thinking. After discussing orientations with different levels of potential, we consider the cases of two teachers to illustrate how a particular collection of thinking-as-a-resource orientations could support or hinder a teacher’s development of the practice of building on student thinking. The work contributes to the field’s understanding of why particular orientations might have more or less potential to support teachers’ development of particular teaching practices. It could also be used as a model for analyzing different collections of orientations and could support mathematics teacher educators by allowing them to better tailor their work to meet teachers’ specific needs.

The Effectiveness of Mathematics Teaching Material Based on Ethnomathematics

The study aims to know the effectiveness of mathematics teaching material used based on ethnomathematics toward mathematical solving problem skill and student critical thinking and to know how student activity on mathematics learning by applying mathematics teaching material based on ethnomathematics. Research method applies a quantitative method with post-test only control design research type. Sampling technique applies cluster random sampling. Data collection technique applies documentation, observation, and test method. Data analysis technique applies quantitative data analysis by using t-test. Based on data analysis result, mathematics teaching material based on ethnomathematics proves effective toward solving problem skill and student mathematical critical thinking. Besides, by applying mathematics teaching material can raise student activity.

Implementation of Problem-Based Learning in terms of Student Mathematical Creative Thinking

One of the goals of mathematics teaching is that students have the ability to think creatively. The ability to think creatively is one of the important factors of learning goals for giving knowledge solely to students will not be much help in everyday life, so learning should be able to develop the attitudes and abilities of students that can help to deal with problems in the future creatively. Creative thinking is a thought process that is able to provide ideas or different ideas that can then be transformed into new knowledge and the answers you need. “Think of creative or divergent thinking is to provide a variety of possible answers based on information supplied by the emphasis on the diversity of answers and suitability”. There are four characteristics of creative thinking, namely: fluency (fluency, lose a lot of ideas), flexibility (flexibility, change perspectives with ease), originality (originality, composing something new), and elaboration (elaboration, another idea developed from an idea). Creative thinking is the focus of observation. Therefore, we need a model of learning appropriate to enhance the creative thinking of students is a model Problem-Based Learning (PBL).

삼각부등식 개념형성을 위한 문제해결 과정에 나타나는 초등학생의 수학적 사고와 교사의 역할

The purpose of this study was to examine the mathematical thinking of elementary school students during the problem-solving process to form the concept of triangle inequality and provide some educational suggestions on teacher roles. Teaching plans were mapped out to teach the concept of triangle inequality to selected fourth-grade elementary school students. A primary test was conducted to analyze their mathematical thinking that took place while they solved given problems to build the concept of triangle inequality. In a secondary test, reactions of mathematical thinking students showed to questions of their teachers were analyzed. As a result, upper-tiered students could think mathematically on their own without questions of their teacher in the stage of understanding problems and in the stage of planning. They then solved these problems. Students in middle and lower tiers found clues through questions of their teachers and then engaged in problem solving. At that time, mathematical thinking of these students depended on types of teacher questions. Even if their mathematical thinking was expressed by themselves, it was confirmed that their mistake could not proceed to the next step. Therefore, when students need to solve problems to frame mathematical concepts, it is advisable for their teacher to provide an opportunity for them to solve these problems on their own.

Investigation of the Noticing Levels of Teachers towards Mathematical Thinking of Students: A Lesson Study Model

Bu calisma ile alti ogretmenin ogrencilerin matematiksel dusunmelerine yonelik farkindalik duzeylerinin incelenmesi amaclanmistir. Arastirmada dort ogretmen ders imecesi mesleki gelisim surecine katilirken, kalan iki ogretmen ise katilmamistir. Mesleki gelisim surecine dâhil olan ogretmenlerle gerceklestirilen ders imecesi calismalari tamamlandiktan yaklasik iki ay sonra, alti ogretmene video kayitlari izletilerek ogretim surecine yonelik degerlendirmelerini rapor haline getirmeleri istenmistir. Nitel arastirma desenlerinden ozel durum (ornek olay) calismasinin kullanildigi calismanin veri toplama araclarini ogretmenlere izletilen video kayitlari, ogretmenlerin degerlendirme raporlari ve ogretmenlerle gerceklestirilen yapilandirilmamis gorusmeler olusturmaktadir. Ogretmenlerin ifadelerine bagli olarak ogretim surecindeki farkindalik duzeylerini yorumlamak amaciyla van Es (2011) tarafindan gelistirilen teorik cerceveden faydalanilmistir. Elde edilen bulgular dogrultusunda, ders imecesi surecine dâhil olan ogretmenlerin farkindalik duzeylerinin surece dahil olmayan ogretmenlerin farkindalik duzeylerinden daha fazla oldugu soylenebilir ve ders imecesi mesleki gelisim surecinin ogrenci dusunusu uzerine ogretmenlerin farkindalik duzeylerini arttirdigini gostermektedir.

Growing of the mathematical thinking imaginative to students in designing of the teaching aids for CWD towards to joyful learning

Government and the private parties had also organized of Special School (SS) and Inclusive School. SS requires of math teachers who were professional in the material, but also master the needs of Children with Disabilities (CwD) in teaching-learning process. The problem: How to design the Teaching Aids for CwD through Extra-Curriculum Training (ECT) activities to Joyful Learning? The purposes of this research: (1) To find new ways how to grow the imaginative in mathematical thinking for students of Mathematics Education. (2) To find a Teaching Aids Design that suitable for CwD who studying in SS. (3) In order to create a Teaching Aids for CwD through activities based on ECT to Joyful Learning. The research method was done by qualitative approach. The research subjects were 6 students of Mathematics Education Study Program of FMIPA UNNES who were interested in attending of the training activities based on ECT. The results: (1) ECT can be a place to grow an Imaginative in Mathematical Thinking of students, (2) created the design of the teaching aids for CwD through activities based on ECT to Joyful Learning as a mirror of the imaginative growth in mathematical thinking for students.

Assessing Mathematical Thinking in Different Type of Primary Schools

Mathematical thinking is an act of sense-making and rest on the processes of generalizing, specializing, convincing and conjecturing. The purpose of this study was to determine the level of mathematical thinking students in primary schools and whether there is any difference in the level of mathematical thinking of students from different types of school. The data was collected from 516 Year 4 students which are from 7 primary schools in the state of Terengganu, Johor, Kedah and Federal Territory. Data were collected using a paper-and-pencil test that were directly administered to the sample. The data was analyzed using descriptive and inferential statistics. Statistical software was used to compute the means (M) and corresponding standard deviations (sd). T-tests were also conducted to determine if there are any significant difference in the levels of mathematical thinking of the students according to the different types of schools. The descriptive analysis of the study revealed that primary school students have inadequate level of mathematical thinking (M= 15.25, sd=7.19) and only 2.5% of the students have achieved the adequate level of mathematical thinking based on the “cut off” score of 30.00. The study also found that the level of mathematical thinking of students from Sekolah Kebangsaan (M = 13.37, sd=6.85) was significantly different than level of mathematical thinking of students from Sekolah Jenis Kebangsaan (Cina) (M = 18.64, sd=1.63) with t (514) =-7.87, p< .05). The analysis further revealed that many students were not able to provide and justified reasoning for their decisions, were not able to make generalization based on the observation of patterns, were not alert that problems can have more than one solution, did not seek for other solutions and were contented with having only one solution.

Assessing Teacher Attentiveness to Student Mathematical Thinking: Validity Claims and Evidence

This article illustrates an argument-based approach to presenting validity evidence for assessment items intended to measure a complex construct. Our focus is developing a measure of teachers’ ability to analyze and respond to students’ mathematical thinking for the purpose of program evaluation. Our validity argument consists of claims addressing connections between our item-development process and the theoretical model for the construct we are trying to measure: attentiveness. Evidence derived from theoretical arguments in conjunction with our multiphased item-development process is used to support the claims, including psychometric evidence of Rasch model fit and category ordering. Taken collectively, the evidence provides support for the claim that our selected-response items can measure increasing levels of attentiveness. More globally, our goal in presenting this work is to demonstrate how theoretical arguments and empirical evidence fit within an argument to support claims about how well a construct is represented, operationalized, and structured.

Teacher Learning Opportunities Provided by Implementing Formative Assessment Lessons: Becoming Responsive to Student Mathematical Thinking

Teachers’ ways of using curriculum materials create not only meaningful learning opportunities for students but also opportunities for teachers to learn and change their teaching practices; however, not enough research has investigated precisely how. This study investigates how teachers’ implementation of innovative curriculum materials specifically designed to support formative assessment practices provides learning opportunities for teachers to become more responsive to student mathematical thinking. 2 teachers’ regular lessons as well as those delivered using the innovative curriculum materials were observed; each teacher was observed over the course of 1 academic year. The analysis of the 2 teachers’ cases demonstrates how their different curriculum adaptation strategies led to different learning opportunities for each of them. Although teachers’ enactment of innovative curriculum materials in class naturally creates opportunities for them to learn about the mathematical content as well as their students’ mathematical thinking, these findings discuss precisely how to promote teacher learning and improvement of teaching practices using formative assessment strategies guided by curriculum materials. The implications in relation to supporting teachers’ instructional improvement while implementing reform-oriented curriculum materials, and to designing curriculum materials facilitating teacher learning, are also discussed.

EXPERIMENTATION OF SPICES LEARNING STRATEGIES WITH THE METHOD OF PROBLEM BASED LEARNING (PBL) TO BUILD MOTIVATION AND THE ABILITY TO THINK LOGICALLY FOR VOCATIONAL SCHOOL STUDENTS

This study aims to expose the interactions that occur in the process of mathematics learning and describe a method of learning motivation and logical mathematical thinking of students in classes. The method used in this research was a quasi-experimental design group post-test. In its implementation, this study uses a class experiment. Qualitative data are obtained in the form of motivational learning scale, whereas the quantitative data in the form of logical thinking ability score using normalized gain. The results showed the existence of a positive interaction during learning. However, learning motivation of students didn’t show a significant improvement. While the logical thinking ability of students after learning of mathematics using the strategy of SPICES with PBL method is in the category is fair. In its implementation, the strategy of SPICES needed support some teachers from several fields of science.

O uso de celulares, tablets e notebooks no ensino da matemática

http://dx.doi.org/10.5007/1981-1322.2016v11n2p318O presente artigo tem como objetivo Identificar o desempenho e raciocínio matemático dos alunos usando aplicativos tecnológicos, apontar as ferramentas tecnológicas adequadas ao auxílio do ensino da matemática, buscando o uso de programas virtuais, celulares, tablets e notebooks, além de averiguar as dificuldades encontradas de aprendizagem. Para isso, foi realizado estudo bibliográfico sobre diversos estudiosos como Moran (2007), Demo (1993), Tajra (2001) e Paiva (2008) e uma pesquisa de campo, no Colégio Estadual Dr. Ives Orlando Lopes da Silva, com alunos do 1º ano do ensino médio. Os usos de tais ferramentas podem desenvolver no aluno uma participação mais ativa e prazerosa no ambiente escolar, levando em conta que o manuseio desses aparelhos fazem o discente sentir-se mais familiarizado na escola, melhorando a qualidade do ensino-aprendizagem. Contudo, essas ferramentas exigem cuidados e acompanhamento por parte do professor, para que o manuseio das mesmas seja aplicado de forma correta e eficaz no desenvolvimento da disciplina.

A RELATIONSHIP BETWEEN PROBLEM SOLVING ABILITY AND STUDENTS’ MATHEMATICAL THINKING

This research have a purpose to know is there an influence of problem solving abilty to students mathematical thinking, and to know how strong problem solving ability affect students mathematical thinking. This research used descriptive quantitative method, which a population is all of students that taking discrete mathematics courses both in department of Information Systems and department of mathematics education. Based on the results of data analysis showed that there are an influence of problem solving ability to students mathematical thinking either at department of mathematics education or at department of information systems. In this study, it was found that the influence of problem solving ability to students mathematical thinking which take place at mathematics education department is stonger than at information system department. This is because, at mathematics education department, problem-solving activities more often performed in courses than at department of information system. Almost 75% of existing courses in department of mathematics education involve problem solving to the objective of courses, meanwhile, in the department of information systems, there are only 10% of these courses. As a result, mathematics education department student’s are better trained in problem solving than information system department students. So, to improve students’ mathematical thinking, its would be better, at fisrtly enhance the problem solving ability.

A RELATIONSHIP BETWEEN PROBLEM SOLVING ABILITY AND STUDENTS’ MATHEMATICAL THINKING

This research have a purpose to know is there an influence of problem solving abilty to students mathematical thinking, and to know how strong problem solving ability affect students mathematical thinking. This research used descriptive quantitative method, which a population is all of students that taking discrete mathematics courses both in department of Information Systems and department of mathematics education. Based on the results of data analysis showed that there are an influence of problem solving ability to students mathematical thinking either at department of mathematics education or at department of information systems. In this study, it was found that the influence of problem solving ability to students mathematical thinking which take place at mathematics education department is stonger than at information system department. This is because, at mathematics education department, problem-solving activities more often performed in courses than at department of information system. Almost 75% of existing courses in department of mathematics education involve problem solving to the objective of courses, meanwhile, in the department of information systems, there are only 10% of these courses. As a result, mathematics education department student’s are better trained in problem solving than information system department students. So, to improve students’ mathematical thinking, its would be better, at fisrtly enhance the problem solving ability.

Learning to notice important student mathematical thinking in complex classroom interactions

Noticing students' mathematical thinking is a key element of effective instruction, but novice teachers do not naturally engage in this practice. Prospective secondary school mathematics teachers were engaged in an intervention grounded in analysis of minimally edited video from local secondary school mathematics classrooms; the goal was to support their ability to notice important student thinking within the complexity of instruction. Evidence of participants' learning in five iterations of the intervention is discussed, including their focus on student mathematical thinking, their ability to discuss the mathematics in that thinking, and their ability to notice particular high-leverage instances of student thinking.

Attributes of Instances of Student Mathematical Thinking that Are Worth Building on in Whole-Class Discussion

ABSTRACTThis study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners’ understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in the moment, the accuracy of the thinking, and the type of thinking (e.g., sense-making). Findings illuminate the complexity of identifying student thinking worth building on during whole-class discussion and provide insight into important attributes of these high potential instances that could be used to help teachers more easily recognize them. Implications for researching, learning, and enacting the teaching practice of building on student mathematical thinking are discussed.

Proses Berpikir Matematis Siswa dalam Menyelesaikan Masalah Matematika di tinjau dari Tipe Kepribadian Keirsey

This study aims to describe the process of mathematical thinking of students in solving mathematical problems in terms of Keirsey's personality type. This research is a qualitative-descriptive research. Research subjects taken are MAN 2 Tulang Bawang Barat class XI students by purposive sampling. Research subjects amounted to 2 people from each personality type. Data collection is done by observation, interview, and documentation. Data validity using technique triangulation. Data analysis techniques used are the concept of Miles and Huberman, namely data reduction, data presentation, and conclusion. The results showed that each of Keirsey's students in solving mathematical problems was more likely to be a student of a Guardian personality type. In solving mathematical problems begins with the acceptance of information marked by understanding the problem involves knowing what is known (M1), knowing what is being asked (M2), knowing the required requirements in problem solving (M3), as well as making the model of math from the problem with its own understanding (M4). Then proceed with the processing of information marked by implementing the problem-solving plan (R1) and proceed with executing the plan to get the answer (P1), but the steps are not complete. While in rechecking the answer (C1) students do re-check, then in drawing a conclusion (C2), students draw conclusions only on some tests.

How can 5 + 6 = 7? Exploring the use of a screening tool to investigate students� mathematical thinking in class two in Kolkata, India

How can 5 + 6 = 7? Exploring the use of a screening tool to investigate students� mathematical thinking in class two in Kolkata, India