An Investigation of Students’ Algebraic Proficiency From a Structure Sense Perspective

Jupri, Al; Sispiyati, Ririn; Chin, Kin Eng

doi:10.22342/jme.12.1.13125.147-158

Cited by 5 publications

(6 citation statements)

References 15 publications

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“…Regarding student difficulties in solving inequalities of task one and two, which related to the use of the procedural strategy, errors in expanding and factorizing algebraic expressions were observed. From the perspective of symbol sense, these difficulties involve an inability in manipulating symbolic expressions in the process of problem solving (Arcavi, 2005;Bokhove and Drijvers, 2010;Jupri and Sispiyati, 2020;Jupri et al, 2021). The difficulties encountered by the students, related to the use of the symbol sense strategy, include errors of canceling out the same factors on both sides of an inequality and therefore, concluding an incorrect solution to the inequality.…”

Section: Discussionmentioning

confidence: 99%

“…Worldwide, algebra is considered a subject that is difficult for most students to learn and for teachers to teach (Bokhove and Drijvers, 2012;Chapman, 2006;Carraher et al, 2006;Van Amerom, 2003), and this is also true in Indonesia (Jupri et al, 2014a;Jupri et al, 2015;. Previous studies investigating student difficulties in understanding early algebra, revealed that Indonesian students lack both algebraic procedural skills and conceptual understanding in dealing with equations, algebraic expressions, and word problems (Jupri et al, 2014a;Jupri et al, 2014b;Jupri et al, 2021). There are several factors that contribute to this, one of which is a lack of either the students or teachers' ability to understand algebra.…”

Section: Introductionmentioning

confidence: 99%

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Prospective Mathematics Teachers’ Algebraic Proficiency From a Symbol Sense Perspective: The Case of Solving Inequalities

2022

JHETP

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Procedural fluency and conceptual understanding are two aspects of mathematical proficiency discussed worldwide, including in Indonesia. In the algebra domain, algebraic proficiency concerns an ability to deal with symbolic representations that can be viewed from a symbol sense perspective. This algebraic proficiency is considered indispensable for prospective mathematics teachers for their future careers. This research aims to analyze prospective mathematics teachers' algebraic proficiency from the perspective of symbol sense. To achieve this aim, we set up a qualitative case study, involving 19 Indonesian mathematics education students (21-23 years old) as prospective mathematics teachers, in the form of a two-week online teaching and learning process (4 x 50 minutes) and its corresponding formative assessment for solving quadratic, cubic, and rational inequalities. The results revealed that the majority of the participants lack algebraic proficiency as they use procedural strategies more than symbol sense strategies to solve inequalities.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Prospective Mathematics Teachers’ Algebraic Proficiency From a Symbol Sense Perspective: The Case of Solving Inequalities

2022

JHETP

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“…Problem-solving accuracy and efficiency are primary goals in mathematics education (Common Core State Standards, 2010); however, many students struggle to acquire structure sense—the ability to detect patterns within mathematical notation (e.g., opposites: 3 + (–3); inverses: 4 × 1/4; like terms: 2( x + y ) and 3( x + y ); groups of terms: a x 2 and b x in a x 2 + b x ), derive meaningful interpretations from the notation, and efficiently act on it (Hoch & Dreyfus, 2004; Jupri et al, 2021; Livneh & Linchevski, 2007). In arithmetic, children and adults often struggle to acquire its structure and fail to consistently follow the order of precedence when performing operations (Landy & Goldstone, 2010; M.…”

Section: Introductionmentioning

confidence: 99%

Resisting the urge to calculate: The relation between inhibitory control and perceptual cues in arithmetic performance

Closser

Chan

Ottmar

2023

Quarterly Journal of Experimental Psychology

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Subtle visual manipulations to the presentation of mathematical notation influence the way that students perceive and solve problems. While there is a consistent impact of perceptual cues on students’ problem solving, other cognitive skills such as inhibitory control may interact with perceptual cues to impact students’ arithmetic problem-solving performance. We present an online experiment in which college students completed a version of the Stroop task followed by arithmetic problems in which the spacing between numbers and operators was either congruent (e.g., 2 + 3×4) or incongruent (e.g., 2+3 × 4) to the order of precedence. We found that students were comparably accurate between problem types but might have spent longer responding to problems with congruent than incongruent spacing. There was no main effect of inhibitory control on students’ performance on these problems. However, an exploratory analysis on a combined performance measure of accuracy and response time revealed an interaction between problem type and inhibitory control. Students with higher inhibitory control performed better on congruent vs. incongruent problems whereas students with lower inhibitory control performed worse on congruent vs. incongruent problems. Together, these results suggest that the relation between inhibitory control and arithmetic performance may not be straightforward. Further, this work advances perceptual learning theory and contributes new findings on the contexts in which perceptual cues, such as spacing, influence arithmetic performance.

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“…Based on the facts, experiences, and observations, when teachers encounter problems regarding professional competencies that require conceptual understanding or problem-solving immediately, formal teacher development is felt to be lacking. Conceptual understanding, particularly in mathematics, includes not procedural understanding but also relational understanding that relates to various mathematical concepts (Jupri et al, 2021;Skemp, 1976). Meanwhile, problem-solving, which needs higher-order thinking skills, requires teachers to think critically, creatively, and non-routinely Koichu & Leron, 2015;Polya, 1973;Posamentier & Stepelman, 1990;Samo, 2017).…”

Section: Introductionmentioning

confidence: 99%

The development of mathematics teacher professional competencies through social media

Jupri

Marwati

Sispiyati

et al. 2022

jel

Self Cite

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One of the competencies for mathematics teachers that needs to be developed continuously is professional competence. However, even if efforts for developing teachers’ competencies have been made formally by the government, it seems still lacking. This study, therefore, aims to develop mathematics teacher professional competencies through an informal development model using social media. This research used a qualitative method, a case study design, involving 19 mathematics teachers from various regions in Indonesia in the informal development process in the range of 2019-2021. The informal approach was carried out using question-and-answer techniques and guided discussions on mathematical problems. From the teacher development processes, 30 mathematics problems and their solutions were collected. As an illustration of this development process, this article presents five problems and their solutions, including solutions for two mathematics problems on conceptual understanding and three mathematics problems on problem-solving. We conclude that this informal approach is fruitful in helping mathematics teachers solve mathematics problems. This study implies that the teacher development process carried out in this study can be used as a model for informal teacher development by other higher education academics in their respective places.

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An Investigation of Students’ Algebraic Proficiency From a Structure Sense Perspective

Cited by 5 publications

References 15 publications

Prospective Mathematics Teachers’ Algebraic Proficiency From a Symbol Sense Perspective: The Case of Solving Inequalities

Prospective Mathematics Teachers’ Algebraic Proficiency From a Symbol Sense Perspective: The Case of Solving Inequalities

Resisting the urge to calculate: The relation between inhibitory control and perceptual cues in arithmetic performance

The development of mathematics teacher professional competencies through social media

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