Development of Problem-Solving Strategies in Repeated Sentence-Verification Tasks

1987 ◽  
Vol 65 (2) ◽  
pp. 655-661 ◽  
Author(s):  
John G. E. Harpur ◽  
Heather M. A. Macleod ◽  
Joy V. Decker
Keyword(s):  
Problem Solving ◽  
Reaction Times ◽  
Response Rates ◽  
Repeated Exposure ◽  
Verification Task ◽  
Problem Types ◽  
Different Types ◽  
General Improvement ◽  
Problem Solving Strategies

This experiment was designed to investigate the development of problem-solving strategies by subjects in a sentence-verification paradigm which permitted repeated exposure to problems of the same type. While it was predicted that subjects would show a general improvement across trials as a function of repeated exposure to similar sets of problems, nevertheless it was predicted that some types of problem would show little or no improvement across trials, while other problems would show significant improvement as the subjects determined more efficient strategies to use to aid in rapid solutions. The results illustrate that certain types of sentence-verification tasks allow the development of efficient strategies which significantly decrease reaction times across trials, while other problem types produce uniform response rates across problem sets with negligible improvement as a function of practice. The results ate interpreted in terms of the relative availability of problem-solving strategies for the different types of verification task.

Inverting the Remedial Mathematics Classroom with Alternative Assessment

2011 ◽  
pp. 205-212
Author(s):  
Victor W. Brunsden
Keyword(s):  
College Student ◽  
Problem Solving ◽  
Alternative Assessment ◽  
Mathematics Classroom ◽  
Remedial Mathematics ◽  
Traditional Lecture ◽  
Problem Types ◽  
Problem Solving Strategies ◽  
Lecture Format

The author present a case-study of a classroom technique that allows assessment and some remediation of several shortcomings of college student skills in mathematics, particularly problem solving. Students are required to write their own notes for class and hand them in at the end for credit. Instead of a traditional lecture format, the first part of class is used to do examples of problems, creating an opportunity to model problem solving strategies for the class. Students then are separated into groups to work on individualized homework sets delivered via WeBWorK and group projects. Although problem sets are individualized, the problem types are the same from student to student, and the groups work on problems from all students in the group. Several issues of implementation are identified. Also discussed are alternative implementations of parts of the strategy, and possible extensions of the strategy to other courses that aren’t based on problem-solving.

IDENTIFICATION OF PROBLEM SOLVING STRATEGIES IN MATHEATICS AMONG HIGH SCHOOL STUDENTS

2017 ◽  
Vol 4 (36) ◽  
Author(s):  
J. Navaneetha Krishnan ◽  
P. Paul Devanesan
Keyword(s):  
High School ◽  
High School Students ◽  
Problem Solving ◽  
Sample Survey ◽  
Survey Method ◽  
Teaching Mathematics ◽  
School Students ◽  
Problem Solving Strategies ◽  
Achievement In Mathematics

The major aim of teaching Mathematics is to develop problem solving skill among the students. This article aims to find out the problem solving strategies and to test the students’ ability in using these strategies to solve problems. Using sample survey method, four hundred students were taken for this investigation. Students’ achievement in solving problems was tested for their Identification and Application of Problem Solving Strategies as a major finding, thirty one percent of the students’ achievement in mathematics is contributed by Identification and Application of Problem Solving Strategies.

scholarly journals Using process data to understand problem-solving strategies and processes for drag-and-drop items in a large-scale mathematics assessment

2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Yang Jiang ◽  
Tao Gong ◽  
Luis E. Saldivia ◽  
Gabrielle Cayton-Hodges ◽  
Christopher Agard
Keyword(s):  
Problem Solving ◽  
Time Allocation ◽  
Large Scale ◽  
Solution Process ◽  
Process Data ◽  
Mathematics Assessments ◽  
Assessment Design ◽  
Eighth Grade Students ◽  
Problem Solving Strategies ◽  
Drag And Drop

AbstractIn 2017, the mathematics assessments that are part of the National Assessment of Educational Progress (NAEP) program underwent a transformation shifting the administration from paper-and-pencil formats to digitally-based assessments (DBA). This shift introduced new interactive item types that bring rich process data and tremendous opportunities to study the cognitive and behavioral processes that underlie test-takers’ performances in ways that are not otherwise possible with the response data alone. In this exploratory study, we investigated the problem-solving processes and strategies applied by the nation’s fourth and eighth graders by analyzing the process data collected during their interactions with two technology-enhanced drag-and-drop items (one item for each grade) included in the first digital operational administration of the NAEP’s mathematics assessments. Results from this research revealed how test-takers who achieved different levels of accuracy on the items engaged in various cognitive and metacognitive processes (e.g., in terms of their time allocation, answer change behaviors, and problem-solving strategies), providing insights into the common mathematical misconceptions that fourth- and eighth-grade students held and the steps where they may have struggled during their solution process. Implications of the findings for educational assessment design and limitations of this research are also discussed.

scholarly journals Teachers’ Use of Technology Affordances to Contextualize and Dynamically Enrich and Extend Mathematical Problem-Solving Strategies

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 793
Author(s):  
Manuel Santos-Trigo ◽  
Fernando Barrera-Mora ◽  
Matías Camacho-Machín
Keyword(s):  
Problem Solving ◽  
High School Teachers ◽  
Digital Technology ◽  
Dynamic Models ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
School Teachers ◽  
Use Of Technology ◽  
Technology Affordances ◽  
Problem Solving Strategies

This study aims to document the extent to which the use of digital technology enhances and extends high school teachers’ problem-solving strategies when framing their teaching scenarios. The participants systematically relied on online developments such as Wikipedia to contextualize problem statements or to review involved concepts. Likewise, they activated GeoGebra’s affordances to construct and explore dynamic models of tasks. The Apollonius problem is used to illustrate and discuss how the participants contextualized the task and relied on technology affordances to construct and explore problems’ dynamic models. As a result, they exhibited and extended the domain of several problem-solving strategies including the use of simpler cases, dragging orderly objects, measuring objects attributes, and finding loci of some objects that shaped their approached to reasoning and solve problems.

scholarly journals Creativity as a function of problem-solving expertise: posing new problems through investigations

ZDM ◽  
2021 ◽  
Author(s):  
Haim Elgrably ◽  
Roza Leikin
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Problem Posing ◽  
Dynamic Geometry Environment ◽  
Mathematics Majors ◽  
Individual Interviews ◽  
University Mathematics ◽  
Domain Specific ◽  
Mathematics Test ◽  
Different Types

AbstractThis study was inspired by the following question: how is mathematical creativity connected to different kinds of expertise in mathematics? Basing our work on arguments about the domain-specific nature of expertise and creativity, we looked at how participants from two groups with two different types of expertise performed in problem-posing-through-investigations (PPI) in a dynamic geometry environment (DGE). The first type of expertise—MO—involved being a candidate or a member of the Israeli International Mathematical Olympiad team. The second type—MM—was comprised of mathematics majors who excelled in university mathematics. We conducted individual interviews with eight MO participants who were asked to perform PPI in geometry, without previous experience in performing a task of this kind. Eleven MMs tackled the same PPI task during a mathematics test at the end of a 52-h course that integrated PPI. To characterize connections between creativity and expertise, we analyzed participants’ performance on the PPI tasks according to proof skills (i.e., auxiliary constructions, the complexity of posed tasks, and correctness of their proofs) and creativity components (i.e., fluency, flexibility and originality of the discovered properties). Our findings demonstrate significant differences between PPI by MO participants and by MM participants as reflected in the more creative performance and more successful proving processes demonstrated by MO participants. We argue that problem posing and problem solving are inseparable when MO experts are engaged in PPI.

scholarly journals Thinking Process of Naive Problem Solvers to Solve Mathematical Problems

2016 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
Jackson Pasini Mairing
Keyword(s):  
Problem Solving ◽  
Procedural Knowledge ◽  
Mental Image ◽  
Research Subjects ◽  
Maximum Score ◽  
Mathematical Problems ◽  
Problem Solving Strategies ◽  
Thinking Process ◽  
Problem Solvers ◽  
Holistic Rubric

Solving problem is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe the thinking process of naive problem solvers based on heuristic of Polya. The researcher gave two problems to students at grade XI from one of high schools in Palangka Raya, Indonesia. The research subjects were two students with problem solving scores of 0 or 1 for both problems (naive problem solvers). The score was determined by using a holistic rubric with maximum score of 4. Each subject was interviewed by the researcher separately based on the subject’s solution. The results showed that the naive problem solvers read the problems for several times in order to understand them. The naive problem solvers could determine the known and the unknown if they were written in the problems. However, they faced difficulties when the information in the problems should be processed in their mindsto construct a mental image. The naive problem solvers were also failed to make an appropriate plan because they did not have a problem solving schema. The schema was constructed by the understanding of the problems, conceptual and procedural knowledge of the relevant concepts, knowledge of problem solving strategies, and previous experiences in solving isomorphic problems.

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