Compare and Discuss Multiple Strategies

A mixture cognitive diagnosis model (CDM), which is called mixture multiple strategy-Deterministic, Inputs, Noisy “and” Gate (MMS-DINA) model, is proposed to investigate individual differences in the selection of response categories in multiple-strategy items. The MMS-DINA model system is an effective psychometric and statistical approach consisting of multiple strategies for practical skills diagnostic testing, which not only allows for multiple strategies of problem solving, but also allows for different strategies to be associated with different levels of difficulty. A Markov chain Monte Carlo (MCMC) algorithm for parameter estimation is given to estimate model, and four simulation studies are presented to evaluate the performance of the MCMC algorithm. Based on the available MCMC outputs, two Bayesian model selection criteria are computed for guiding the choice of the single strategy DINA model and multiple strategy DINA models. An analysis of fraction subtraction data is provided as an illustration example.

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Using Writing Strategies in Math to Increase Metacognitive Skills for the Gifted Learner

Gifted Child Today ◽

10.1177/1076217516675904 ◽

2017 ◽

Vol 40 (1) ◽

pp. 43-47 ◽

Cited By ~ 7

Author(s):

Heather Knox

Keyword(s):

Academic Success ◽

Problem Solving ◽

Mathematics Classroom ◽

Metacognitive Skills ◽

Problem Solving Skills ◽

Gifted Learners ◽

Solution Strategies ◽

Multiple Strategies ◽

Problem Solving Process ◽

Metacognitive Ability

Metacognition is vital for a student’s academic success. Gifted learners are no exception. By enhancing metacognition, gifted learners can identify multiple strategies to use in a situation, evaluate those strategies, and determine the most effective given the scenario. Increased metacognitive ability can prove useful for gifted learners in the mathematics classroom by improving their problem-solving skills and conceptual understanding of mathematical content. Implemented effectively, writing is one way to increase a student’s metacognitive ability. Journal writing in the mathematics classroom can help students by clarifying their thought process while further developing content knowledge. Implementing writing can lead to increased understanding of the problem, identification of additional strategies that can be used to solve the problem, and reflective thinking during the problem-solving process. Reflective writing in mathematics can help students evaluate solution strategies and identify strengths and areas of improvement in their mathematical understanding.

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The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem-solving lesson

Journal of Mathematics Teacher Education ◽

10.1007/s10857-021-09511-6 ◽

2022 ◽

Author(s):

Fay Baldry ◽

Jacqueline Mann ◽

Rachael Horsman ◽

Dai Koiwa ◽

Colin Foster

Keyword(s):

Problem Solving ◽

Teaching Practice ◽

Careful Planning ◽

Student Responses ◽

Research And Teaching ◽

Mathematical Discussions ◽

Solution Methods ◽

Multiple Alternative ◽

Productive Discussion ◽

Alternative Solutions

AbstractIn this paper, we analyse a grade 8 (age 13–14) Japanese problem-solving lesson involving angles associated with parallel lines, taught by a highly regarded, expert Japanese mathematics teacher. The focus of our observation was on how the teacher used carefully planned board work to support a rich and extensive plenary discussion (neriage) in which he shifted the focus from individual mathematical solutions to generalised properties. By comparing the teacher’s detailed prior planning of the board work (bansho) with that which he produced during the lesson, we distinguish between aspects of the lesson that he considered essential and those he treated as contingent. Our analysis reveals how the careful planning of the board work enabled the teacher to be free to explore with the students the multiple alternative solution methods that they had produced, while at the same time having a clear overall purpose relating to how angle properties can be used to find additional solution methods. We outline how these findings from within the strong tradition of the Japanese problem-solving lesson might inform research and teaching practice outside of Japan, where a deep heritage of bansho and neriage is not present. In particular, we highlight three prominent features of this teacher’s practice: the detailed lesson planning in which particular solutions were prioritised for discussion; the considerable amount of time given over to student generation and comparison of alternative solutions; and the ways in which the teacher’s use of the board was seen to support the richness of the mathematical discussions.

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Teacher’s instruction in the reflection phase of the problem solving process

LUMAT International Journal on Math Science and Technology Education ◽

10.31129/lumat.v3i1.1051 ◽

2015 ◽

Vol 3 (1) ◽

pp. 55-68

Author(s):

Meira Koponen

Keyword(s):

Problem Solving ◽

Mathematical Thinking ◽

Mathematical Problem ◽

Fifth Grade ◽

Mathematical Problem Solving ◽

Classroom Discussions ◽

Reflection Phase ◽

Mathematical Discussions ◽

Wrong Direction ◽

Problem Solving Process

Mathematical problem solving has a key part in developing students’ mathematical thinking. Yet in the Finnish primary school classrooms mathematics lessons are very traditional and have little room for problem solving and mathematical discussions. Although problem solving has been a part of the Finnish curriculum for a few decades, it is the teachers who seem to choose not to include problem solving in the classroom on a regular basis. In this article I take a look at three Finnish fifth grade teachers who took part in a study on problem solving. They each incorporated problem solving in their mathematics lessons approximately once a month, and in this study I focused on one of the problems – an open problem called “The Labyrinth”. In each lesson I chose to focus on the teachers’ instruction in the reflection phase of the problem solving process. When instructing individual students in the reflection phase and during whole-classroom discussions, the teacher has an opportunity to point out the important parts of the problem solving process, help the students make connections and recall key moments of the process. In the reflection phase there is an opportunity to reflect, review and analyze one’s solutions and make generalizations. In the Labyrinth problem the teacher’s own understanding of the solution was an important factor during the instruction and the whole-classroom discussion. If the teacher’s instruction was purely led by the students’ own discoveries and insights, some important points were left unexplored. The teacher can even lead the students to the wrong direction, if he or she hasn’t carefully thought through the solution of the problem beforehand. The problem solving lesson is not just about finding a suitable problem and presenting it to the students, but guiding the students in the process.

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The Problem-Solving Box: A Novel Task for Assessing Executive Functions in 1.5- to 4-year-olds

10.31219/osf.io/srafv ◽

2018 ◽

Author(s):

Alexandra Hendry ◽

Mary A. Agyapong ◽

Hana D'Souza ◽

Matilda A. Frick ◽

Ana Maria Portugal ◽

...

Keyword(s):

Problem Solving ◽

Executive Functions ◽

Developmentally Appropriate ◽

Relative Strength ◽

Typically Developing ◽

Multiple Strategies ◽

Age Related ◽

Dimensional Measure ◽

Problem Solvers ◽

Problem Solving Task

Executive Functions (EFs) underpin the ability to work towards goals by co-ordinating thought and action. Difficulties with EF are implicated in many neurodevelopmental disorders. Research into the early development and remediation of EF difficulties has been hampered by a scarcity of measures suitable for very young children. We introduce a novel problem-solving task involving a box containing 3 visible rewards. Retrieval of all 3 rewards requires generation of multiple strategies, inhibition of previously-successful strategies, and persistence despite set-backs. The task requires integrative application of EFs, and mirrors the un-structured nature of real-world tasks. Exploratory analysis of data from 110 typically-developing British and Swedish children who attempted this 5-minute task indicates the task is developmentally appropriate for 1.5- to 4-year-olds. Preschoolers were more successful problem-solvers than toddlers. Age-related improvements were observed for generativity and persistence, but age was not associated with perseveration. Boys achieve higher overall scores, and were less perseverative, than girls. The low social and language demands of the task, and the ability to identify areas of relative strength and weakness even when success is not fully achieved, are markers of the task’s potential as a dimensional measure of early EF skills.

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Multiple Strategies: Product of Reasoning and Communication

The Arithmetic Teacher ◽

10.5951/at.40.7.0380 ◽

1993 ◽

Vol 40 (7) ◽

pp. 380-386

Author(s):

Alice J. Gill

Keyword(s):

Mathematics Education ◽

Problem Solving ◽

Communication Skills ◽

Business Community ◽

Curriculum Standards ◽

Evaluation Standards ◽

Multiple Strategies ◽

Multiple Strategy

The NCTM's Curriculum and Evaluation Standards (1989) supports the idea that problems can be solved in more than one correct way. This multiple-strategy approach contains the seeds of motivation, success, and mind stretching. The curriculum standards that focus on reasoning and communication skills are integral to delivering mathematics education that generates the cre ative, problem-solving, divergent thinker that the business community would like to employ.

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Teacher to Teacher: Use Color to Assess Mathematics Problem Solving

The Arithmetic Teacher ◽

10.5951/at.41.6.0307 ◽

1994 ◽

Vol 41 (6) ◽

pp. 307-308

Author(s):

Margaret Biggerstaff ◽

Barb Halloran ◽

Carolyn Serrano

Keyword(s):

Problem Solving ◽

Multiple Solutions ◽

Mathematics Instruction ◽

Authentic Assessment ◽

Mathematics Problem Solving ◽

Multiple Strategies ◽

Teacher Use ◽

Mathematics Problem

Authentic assessment aligned with the curriculum is changing expectations of students' work in mathematics. The move away from one right answer to multiple solutions and multiple strategies in mathematics problem solving requires a way to increase students' awareness about expectations and increase their competence. Students need to know the criteria that will be used to measure their mathematics problem-solving work. Equitable mathematics instruction includes ensuring that all students understand the purposes, standards, and processes of assessment.

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