scholarly journals SECONDARY MATHEMATICS PRESERVICE TEACHERS’ CONCEPTION ABOUT AUTHENTICITY OF MATHEMATICAL TASKS

2019 ◽  
Vol 128 (6B) ◽  
pp. 5
Author(s):  
Nguyễn Thị Tân An ◽  
Tạ Thị Minh Phương ◽  
Nguyễn Thị Duyến ◽  
Trần Ngọc Đức Toàn ◽  
Trần Dũng
Keyword(s):  
Preservice Teachers ◽  
Teaching And Learning ◽  
Secondary Mathematics ◽  
Research Literature ◽  
Positive Interactions ◽  
Teaching Approaches ◽  
Life Problems ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Authenticity In Teaching

The teaching approaches of mathematics derived from humanity involve positive interactions that support meaningful and relevant learning. The main objective of the teaching approaches is to prepare students with the competence to solve daily life problems and one of the most important tools is using authentic tasks. There are different opinions on "task authenticity" in teaching and learning mathematics. This study examined how secondary mathematics preservice teachers think of the authenticity of tasks. Drawing on a framework of tasks authenticity adopted from the research literature, we analyzed PSTs’ response to the criteria of task authenticity. The results show that the PSTs attended to the event feature and the tool feature of task, but overlooked other features. Implications for teacher training are discussed.

Visions of the Possible: Using Drawings to Elicit and Support Visions of Teaching Mathematics

2020 ◽  
Vol 8 (2) ◽  
pp. 59-80
Author(s):  
Jennifer Ruef
Keyword(s):  
Preservice Teachers ◽  
Teaching And Learning ◽  
Teacher Educators ◽  
Teacher Education Program ◽  
Teaching Mathematics ◽  
Nctm Standards ◽  
Mathematics Teacher Educators ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
One Year

Mathematics Teacher Educators (MTEs) help preservice teachers in transitioning from students to teachers of mathematics. They support PSTs in shifting what they notice and envision to align with the collective vision encoded in the AMTE and NCTM standards. This study analyzes drawings and descriptions completed at the beginning and end of a one-year teacher education program—snapshots depicting optimized visions of teaching and learning mathematics. This study analyzed drawings-and-descriptions by cohort and by participants. The findings suggest that the task can be used as formative assessment to inform supports for specific PSTs such as choosing a cooperating teacher or coursework that challenges problematic beliefs. It can also be used as summative assessment to inform revision of coursework for the next cohort.

Teaching and Learning Mathematics Visually or Verbally: A Comparison of Two Teaching Approaches and Investigation of Interactions With Pupil Cognitive Style

2006 ◽  
Vol 5 (3) ◽  
pp. 288-309 ◽  
Author(s):  
Pamela Woolner
Keyword(s):  
Cognitive Style ◽  
Cognitive Abilities ◽  
Teaching And Learning ◽  
Teaching Style ◽  
Teaching Approaches ◽  
Post Intervention ◽  
Visual Spatial ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Positive Correlations

Despite mathematicians’ valuing the ability to visualize a problem and psychologists’ finding positive correlations of visual-spatial ability with success in mathematics, many educationists remain unconvinced about the benefits of visualization for mathematical understanding. One reason for this is evidence that students considered to be visualizers tend to have specific problems with the subject. In this research, “visual” and “verbal” teaching approaches were compared through teaching a range of early secondary school mathematics topics to two classes using one or the other approach. The pupils were assessed using measures of specific cognitive abilities and of visualizer-verbalizer cognitive style. The two classes were compared through a post-intervention test of mathematical competency, on which the verbally taught class scored significantly higher. No interactions were found between teaching style and the learner’s preferred style although the pupils identified as “visualizers” did tend to perform less well.

scholarly journals Frame shifting as a challenge to integrating computational thinking in secondary mathematics education

2020 ◽  
Author(s):  
Wendy Huang
Keyword(s):  
Teaching And Learning ◽  
Computational Thinking ◽  
Secondary Mathematics ◽  
Secondary Mathematics Education ◽  
12Th Grade ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Subject Specific ◽  
And Mathematics

In this study, we adapted the notion of framing, a theoretical construct that refers to a person’s expectations about social spaces (Goffman, 1974), to investigate whether teachers viewed computational thinking (CT) according to subject-specific frames. This case study aimed to understand how teachers make connections between CT and subjects targeted for integration. Epistemological framing contributed new insights on why teachers connected CT in different ways to different subjects: frame shifting focused teachers’ attention on goals and activities specific to each subject. As teachers attended to a subject’s particularities, they drew upon different epistemic resources to construct their descriptions of CT. Our participants (n=6) were teachers who taught 7th-12th grade computing and mathematics as individual subjects. Qualitative coding of interview transcripts revealed that teachers' ideas about CT in computing were strongly influenced by computer programming while their ideas about CT in mathematics corresponded with familiar ways of teaching and learning mathematics. However, rather than accepting the fragmentation of CT as the price of integration into individual subjects, we propose limiting the scope when defining CT. We explain how this non-intuitive strategy can preserve the coherence of CT and how it might be used in CT professional development (PD) for mathematics teachers.

scholarly journals Problematizing teaching and learning mathematics as “given” in STEM education

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Yeping Li ◽  
Alan H. Schoenfeld
Keyword(s):  
Mathematics Education ◽  
Stem Education ◽  
Teaching And Learning ◽  
Science Technology ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Alternative Approach ◽  
And Mathematics ◽  
Scientific Engineering

AbstractMathematics is fundamental for many professions, especially science, technology, and engineering. Yet, mathematics is often perceived as difficult and many students leave disciplines in science, technology, engineering, and mathematics (STEM) as a result, closing doors to scientific, engineering, and technological careers. In this editorial, we argue that how mathematics is traditionally viewed as “given” or “fixed” for students’ expected acquisition alienates many students and needs to be problematized. We propose an alternative approach to changes in mathematics education and show how the alternative also applies to STEM education.

Teaching and Learning Mathematics

1987 ◽  
Vol 71 (458) ◽  
pp. 314
Author(s):  
Paul Ernest ◽  
Peter G. Dean
Keyword(s):  
Teaching And Learning ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics

scholarly journals A Study of Errors and Misconceptions in the Learning of Addition and Subtraction of Directed Numbers in Grade 8

SAGE Open ◽  
2016 ◽  
Vol 6 (4) ◽  
pp. 215824401667137 ◽  
Author(s):  
Judah Paul Makonye ◽  
Josiah Fakude
Keyword(s):  
Conceptual Understanding ◽  
Teaching And Learning ◽  
Study Data ◽  
Negative Numbers ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Number Lines ◽  
Addition And Subtraction ◽  
Logical Errors ◽  
Grade 8

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp’s notions of relational and instrumental understanding of mathematics and Sfard’s participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners’ exercise book responses to directed numbers tasks as well as through interviews. Content analysis was based on Kilpatrick et al.’s strands of mathematical proficiency. The findings were as follows: 83.3% of learners have misconceptions, 16.7% have procedural errors, 67% have strategic errors, and 28.6% have logical errors on addition and subtraction of directed numbers. The sources of the errors seemed to be lack of reference to mediating artifacts such as number lines or other real contextual situations when learning to deal with directed numbers. Learners seemed obsessed with positive numbers and addition operation frames—the first number ideas they encountered in school. They could not easily accommodate negative numbers or the subtraction operation involving negative integers. Another stumbling block seemed to be poor proficiency in English, which is the language of teaching and learning mathematics. The study recommends that building conceptual understanding on directed numbers and operations on them must be encouraged through use of multirepresentations and other contexts meaningful to learners. For that reason, we urge delayed use of calculators.

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