scholarly journals Not all Equals are Equal: Decoupling Thinking Processes and Results in Mathematical Assessments

2019 ◽  
pp. 631-636
Author(s):  
Stephen Woodcock
Keyword(s):  
Mathematics Education ◽  
Specific Question ◽  
Transferable Skills ◽  
Mathematical Thought ◽  
Initial Work ◽  
Thinking Processes ◽  
Positive Integers ◽  
Mathematical Assessments

One of the greatest challenges in mathematics education is in fostering an understanding of what mathematicians would recognise as “mathematical thought.” We seek to encourage students to develop the transferable skills of abstraction, problem generalization and scalability as opposed to simply answering the specific question posed. This difference is perhaps best illustrated by the famous – but likely apocryphal – tale of Gauss’s school days and his approach to summing all positive integers up to and including 100, rather than just summing each sequentially. Especially with the rise of technology-enabled marking and results-focussed tutoring services, the onus is on the educator to develop new types of question which encourage and reward the development of mathematical processes and deprioritise results alone. Some initial work in this area is presented here.

scholarly journals The Effect of Realistic Mathematics Education on Sixth Grade Students’ Statistical Thinking

2021 ◽  
Vol 14 (1) ◽  
pp. 76-90
Author(s):  
Bedriye ALTAYLAR ◽  
Sibel KAZAK
Keyword(s):  
Mathematics Education ◽  
Sixth Grade ◽  
Control Group ◽  
Realistic Mathematics Education ◽  
Statistical Thinking ◽  
Mathematics Textbook ◽  
Realistic Mathematics ◽  
Sixth Grade Students ◽  
Quasi Experimental ◽  
Thinking Processes

Abstract: Purpose of the study is to investigate the effectiveness of the use of Realistic Mathematics Education (RME) approach on sixth grade students’ statistical thinking levels. Mooney’s (2002) statistical thinking framework describing four thinking levels across four different statistical thinking processes was used. This study utilized a quasi-experimental pretestposttest design. In the experimental group, the data handling unit was taught using RME approach whereas in the control group lessons were taught traditionally using a mathematics textbook and direct instruction. A statistical thinking test composed of seven open-ended questions was prepared and applied to both groups as pretest and posttest. The change of students’ statistical thinking levels in pretest and posttest were analyzed and compared in both groups as well as between groups. The data analysis showed that the overall growth at Level 4 across statistical thinking processes was higher for the students who were taught using the RME approach than for those taught traditionally.

scholarly journals Undergraduate Mathematics Education: Teaching Mathematical Thinking Or Product Of Mathematical Thought?

1997 ◽  
pp. 23-40
Author(s):  
Yudariah Mohammad Yusof
Keyword(s):  
Mathematics Education ◽  
Mathematical Thinking ◽  
Undergraduate Mathematics Education ◽  
Undergraduate Mathematics ◽  
Body Of Knowledge ◽  
Mathematical Thought ◽  
Intellectual Independence

This paper reports on an investigation into students' thinking about mathematics and their mathematical behaviour when faced with a problem. It is found that students perceived mathematics as a fixed body of knowledge to be learned. When solving a problem, students demonstrate little intellectual independence and lack the ability to think for themselves. This is a matter of some concern. The findings indicate that the mathematical environment may not be providing students with the experiences to encourage them to be creative and reflective. It is suggested that mathematicians need to move away from teaching students the product of mathematical thought to teaching them mathematical thinking.

Authentic Choice in Mathematical Assessments

2021 ◽  
Vol 114 (4) ◽  
pp. 338-339
Author(s):  
Shraddha Shirude
Keyword(s):  
Mathematics Education ◽  
Mathematical Assessments

Ear to the Ground features voices from various corners of the mathematics education world.

scholarly journals Advanced Mathematic Thinking Ability Based on The Level of Student's Self-Trust in Learning Mathematic Discrete

2020 ◽  
Vol 10 (2) ◽  
pp. 12
Author(s):  
Yemi Kuswardi ◽  
Budi Usodo ◽  
Sutopo Sutopo ◽  
Henny Ekana Chrisnawati ◽  
Farida Nurhasanah
Keyword(s):  
Mathematics Education ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Thinking Skills ◽  
Discrete Mathematics ◽  
Mathematical Representation ◽  
Advanced Mathematical Thinking ◽  
Self Confidence ◽  
Thinking Ability ◽  
Thinking Processes

<p class="BodyAbstract">Mathematical thinking and self-confidence are indispensable aspects of learning mathematics and are influential in solving mathematical problems. In higher education mathematics learning, advanced mathematical thinking skills are required (Advance Mathematical Thinking. Advanced mathematical thinking processes include: 1) mathematical representation, 2) mathematical abstraction, 3) connecting mathematical representation and abstraction, 4) creative thinking, and 5) mathematical proof. Discrete mathematics is one of the courses in mathematics education FKIP UNS. The problems in Discrete Mathematics courses are usually presented in the form of contextual problems. Students often experience difficulties in making mathematical expressions and mathematical abstractions from these contextual problems. In addition, students also experience difficulties in bookkeeping. Most students often prove by using examples of some real problems. Even though proof in mathematics can be obtained by deductive thinking processes or inductive thinking processes, the truth is that mathematics cannot only come from the general assumption of inductive thinking. Based on this, a qualitative descriptive study was carried out which aims to determine the advanced mathematical thinking skills based on the level of student self-confidence. Research with the research subjects of FKIP UNS Mathematics Education Students in Discrete Mathematics learning for the 2019/2020 school year gave general results that the student's ability in advanced mathematical thinking was strongly influenced by the level of student confidence in learning. The higher the student's self-confidence level, the better the student's advanced mathematical thinking ability, so that high self-confidence has a great chance of being successful in solving math problems.</p>

scholarly journals Young Children Representing Numbers: What Does the Literature Say?

2015 ◽  
Vol 39 (3) ◽  
pp. 5
Author(s):  
Gabriela Arias de Sanchez
Keyword(s):  
Early Childhood ◽  
Mathematics Education ◽  
Young Children ◽  
Early Childhood Educators ◽  
Young Age ◽  
Conceptual Frameworks ◽  
Early Childhood Mathematics ◽  
Educational Settings ◽  
Pedagogical Principles ◽  
Mathematical Assessments

Children are exposed to written numerals from a very young age, and the practice of using written numerals is encouraged in early childhood educational settings. Further, many mathematical assessments are based on young children’s understanding of conventional numerals. Supported by socio-constructivist ideas, this review summarizes a body of research in the areas of symbolic and numeric development in young children, providing a synthesis for early childhood educators and teachers. This work is an invitation to reflect on both the pedagogical principles that underline “pencil-pushing practices” and the conceptual frameworks that support current early childhood mathematics education.

scholarly journals STAGES IN PARTIAL FUNCTIONAL THINKING IN THE FORM OF LINEAR FUNCTIONS: APOS THEORY

2020 ◽  
Vol 8 (3) ◽  
pp. 536-544
Author(s):  
Suci Yuniati ◽  
Toto Nusantara ◽  
Subanji ◽  
I Made Sulandra
Keyword(s):  
Mathematics Education ◽  
Linear Functions ◽  
Apos Theory ◽  
Functional Thinking ◽  
Mathematical Problems ◽  
Thinking Processes

Purpose of the study: The purpose of this study is to describe students' partial functional thinking processes in solving mathematical problems based on APOS Theory. The problem in this study was formulated into the question, what are the stages of students' partial functional thinking in solving mathematical problems based on APOS Theory?. Methodology: This study was conducted by with 44 students from the Department of Mathematics Education. The subjects of this study were asked to solve mathematical problems developed from (Wilkie, 2014). Then some of them were interviewed to learn their functional thinking processes. The subjects’ partial functional thinking processes were analyzed using APOS theory. Main Findings: The results showed that, based on APOS theory, the students’ partial functional thinking consisted of several stages: 1) identifying the problem, 2) organizing the data, 3) determining the recursive patterns, 4) determining the covariational relationships, 5) generalizing the relationships between variations in quantities (correspondence), and 6) re-checking the generalization results. In this case, the students generalized the relationships between variations in the form of functions done partially using the arithmetic formula . Applications of this study: The findings of this study can help teachers understand the stages in students' thinking processes in solving problems about functions and the difficulty faced by the students in understanding the functions. Novelty/Originality of this study: The researchers identified stages in students' partial functional thinking in solving mathematical problems in the form of functions based on APOS Theory.

Attitudes towards transferable skills in medical undergraduates

2001 ◽  
Vol 35 (2) ◽  
pp. 148-153 ◽  
Author(s):  
Sue R Whittle ◽  
Deborah G Murdoch Eaton
Keyword(s):  
Transferable Skills ◽  
Medical Undergraduates
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