Interference of Instrumental Instruction in Subsequent Relational Learning

Pesek, Dolores D.; Kirshner, David

doi:10.2307/749885

Cited by 68 publications

(47 citation statements)

References 18 publications

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“…Pesek and Kirshner (2000) conducted an experimental study of two groups (approximately 50 grade 5 students in each group), where one group was taught instrumental knowledge before relational knowledge (formulas were given and trained, without providing explanations of why they worked), while the other group was taught only relational knowledge (together with the "instrumental" group). The results from pre-, post-, and retention tests, along with student interviews, showed that the "relation" group performed better than the "instrumental" group on items involving both conceptual and procedural tasks.…”

Section: The Conceptual-procedural Distinction In Mathematics Educationmentioning

confidence: 99%

Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum: Student Conceptions and Performance

Engelbrecht

Bergsten

Kågesten

2012

J of Engineering Edu

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BACKGROUNDDemands by engineering faculties of mathematics departments have traditionally been for teaching computational skills while also expecting analytic and creative knowledge-based skills. We report on a project between two institutions, one in South Africa and one in Sweden, that investigated whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than the traditional more procedurally oriented way of teaching. PURPOSE (HYPOTHESIS)We focus on how second-year engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between Swedish and South African groups of students in answering conceptual and procedural mathematics problems. We also compare these students' conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. DESIGN/METHODAn instrument consisting of procedural and conceptual items as well as items on student opinions on the roles of the different types of knowledge in their studies was conducted with groups of second-year engineering students at two universities, one in each country. RESULTSAlthough differences between the two countries are small, Swedish students see procedural items to be more common in their mathematics studies while the South African students find both conceptual and procedural items common; the latter group see the conceptually oriented items as more common in their studies outside the mathematics courses. CONCLUSIONSStudents view mathematics as procedural. Conceptual mathematics is seen as relevant outside mathematics. The use of mathematics in other subjects within engineering education can be experienced differently by students from different institutions, indicating that the same type of education can handle the application of mathematics in different ways in different institutions.

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Section: The Conceptual-procedural Distinction In Mathematics Educationmentioning

confidence: 99%

Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum: Student Conceptions and Performance

Engelbrecht

Bergsten

Kågesten

2012

J of Engineering Edu

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“…Task-based approaches that help children unpack the key statistical concepts at hand can be considered indicative of higher levels of knowledge of content and teaching, since such approaches engage children in constructing their own knowledge through problem-solving. Children who are given opportunities to do so often have higher levels of achievement than those who do not (Boaler 1998;Carpenter, Fennema, Peterson, Chiang, and Loef 1989;Pesek and Kirshner 2000). …”

Section: Types Of Individualized Support Suggested For Studentmentioning

confidence: 99%

Using Work Samples from the National Assessment of Educational Progress (NAEP) to Design Tasks that Assess Statistical Knowledge for Teaching

Groth

2014

Journal of Statistics Education

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Statistics courses for prospective teachers are being developed in response to recent K-12 curriculum recommendations. As these courses are developed, it is important to design accompanying assessments. This manuscript describes a strategy for assessing aspects of statistical knowledge for teaching. The strategy involves analyzing and responding to children's work samples from the National Assessment of Educational Progress. An example is provided to illustrate how such an assessment task can serve to reveal different aspects of respondents' subject matter knowledge as well as their pedagogical content knowledge. Thoughts are provided on how to use the assessment tasks to identify levels of statistical knowledge for teaching.

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“…This study examined each of these areas. Adult Indeed, prior research has found that learning procedures prior to development of conceptual understanding interferes with this development (Pesek & Kirshner, 2000).…”

Section: Advancing a Research Agenda In Community College Mathematicsmentioning

confidence: 99%

Adult Returning Students and Proportional Reasoning: Rich Experience and Emerging Mathematical Proficiency

Sitomer

2000

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This study explores adult returning students' mathematical experience and ways of thinking prior to enrolling in a community college arithmetic review course. It further examines one student's experience of the course. The first part of the study documents everyday activities adult students perceive as mathematical using Bishop's pan-cultural mathematical activities (Bishop, 1994), and queries students' prior experience with mathematics in school. The second part examines students' ways of thinking about proportion prior to instruction, using a framework developed from previous research (e.g., Lamon, 1993). The third part of the study examines the interaction between

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Interference of Instrumental Instruction in Subsequent Relational Learning

Cited by 68 publications

References 18 publications

Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum: Student Conceptions and Performance

Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum: Student Conceptions and Performance

Using Work Samples from the National Assessment of Educational Progress (NAEP) to Design Tasks that Assess Statistical Knowledge for Teaching

Adult Returning Students and Proportional Reasoning: Rich Experience and Emerging Mathematical Proficiency

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