The Function Concept with Microcomputers: Multiple Strategies in Problem Solving

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.

Download Full-text

Inequalities, Absolute Value, and Logical Connectives

Mathematics Teacher ◽

10.5951/mt.85.9.0756 ◽

1992 ◽

Vol 85 (9) ◽

pp. 756-757

Author(s):

Charles R. Parish

Keyword(s):

Problem Solving ◽

Function Concept ◽

Real Numbers ◽

Appropriate Use ◽

Standard Definition ◽

Absolute Value ◽

Algebra Students ◽

Logical Connectives ◽

Definition Of ◽

Ordered Pairs

Algebra students often have difficulty in sorting out and correctly using the concepts involved in the solution of linear inequalities. The introduction of the concept of absolute value causes additional complications for many students. Two of the major problem areas are (1) the concept of absolute value as normally defined and (2) the recognition and appropriate use of the logical connectives and and or in the solution of problems that combine inequalities with absolute value. One way to alleviate students' confusion and promote their problem-solving ability in such a setting is to adopt an approach different from that found in current textbooks. This approach involves consideration of the function concept as the graph generated by associated ordered pairs of real numbers rather than functional values as obtained from the standard definition of absolute value.

Download Full-text

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.

Download Full-text

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.

Download Full-text

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.

Download Full-text

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.

Download Full-text

Compare and Discuss Multiple Strategies

Mathematics Teacher ◽

10.5951/mtlt.2021.0051 ◽

2021 ◽

Vol 114 (11) ◽

pp. 853-859

Author(s):

Jon R. Star ◽

Soobin Jeon ◽

Rebecca Comeford ◽

Patricia Clark ◽

Bethany Rittle-Johnson ◽

...

Keyword(s):

Problem Solving ◽

Multiple Strategies ◽

Mathematical Discussions

CDMS is a routine that allows teachers to organize instruction around students’ mathematical discussions and multiple problem-solving methods.

Download Full-text

The investigation of process of teaching function concept in an Adidactic learning environment

Pegem Eğitim ve Öğretim Dergisi ◽

10.14527/pegegog.2018.019 ◽

2018 ◽

Vol 8 (3) ◽

pp. 469-502

Author(s):

Filiz Tuba Dikkartin Övez ◽

Nazlı Akar

Keyword(s):

Problem Solving ◽

Learning Environment ◽

Descriptive Analysis ◽

Function Concept ◽

Situation Theory ◽

High Interaction ◽

Teaching Function ◽

Ninth Grade Students ◽

Five Phases ◽

The Given

This study investigates the learning of the concept of functions in an adidactic learning environment, explains the five phases of the adidactic learning environments defined in the Didactic Situation Theory and their interactions with the milieu generated within the given problem state of the students. It was carried out with 33 ninth grade students from an Anatolian high school in Balıkesir. This qualitative study was designed as a case study. Descriptive analysis was used to analyze the data from students’ worksheets, and the transcriptions of video records in order to investigate the outcomes of an adidactic learning environment in detail. Students’ performances in the teaching process were evaluated with a checklist for problem-solving, construction of function knowledge and interaction with the milieu. The results showed that the basic conditions of an adidactic learning environment were provided, the students with a high interaction with the milieu constructed function knowledge by completing each stage. The students’ display rates for the indicators on the checklist were 70.90 % for problem-solving, 77.77% for construction of function knowledge, and 80.00% for interaction with the milieu.

Download Full-text