scholarly journals Strategic competence for multistep fraction word problems: an overlooked aspect of mathematical knowledge for teaching

2021 ◽  
Author(s):  
Yasemin Copur-Gencturk ◽  
Tenzin Doleck
Keyword(s):  
Word Problem ◽  
Word Problems ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Mathematics Learning ◽  
Mathematical Knowledge For Teaching ◽  
Important Indicator ◽  
Strategic Competence ◽  
The Usa ◽  
Valid Solution

AbstractPrior work on teachers’ mathematical knowledge has contributed to our understanding of the important role of teachers’ knowledge in teaching and learning. However, one aspect of teachers’ mathematical knowledge has received little attention: strategic competence for word problems. Adapting from one of the most comprehensive characterizations of mathematics learning (NRC, 2001), we argue that teachers’ mathematical knowledge also includes strategic competence, which consists of devising a valid solution strategy, mathematizing the problem (i.e., choosing particular strategies and presentations to translate the word problem into mathematical expressions), and arriving at a correct answer (executing a solution) for a word problem. By examining the responses of 350 fourth- and fifth-grade teachers in the USA to four multistep fraction word problems, we were able to explore manifestations of teachers’ strategic competence for word problems. Findings indicate that teachers’ strategic competence was closely related to whether they devised a valid strategy. Further, how teachers dealt with known and unknown quantities in their mathematization of word problems was an important indicator of their strategic competence. Teachers with strong strategic competence used algebraic notations or pictorial representations and dealt with unknown quantities more frequently in their solution methods than did teachers with weak strategic competence. The results of this study provide evidence for the critical nature of strategic competence as another dimension needed to understand and describe teachers’ mathematical knowledge.

Mathematics Teachers' Enactment of Cognitively Demanding Tasks: Investigating Links to Teachers' Knowledge and Conceptions

2014 ◽  
Vol 45 (5) ◽  
pp. 636-674 ◽  
Author(s):  
Anne Garrison Wilhelm
Keyword(s):  
Middle School ◽  
Mathematics Teachers ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Mathematical Knowledge For Teaching ◽  
Middle School Mathematics ◽  
Knowledge For Teaching ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Cognitively Demanding Tasks

This study sought to understand how aspects of middle school mathematics teachers' knowledge and conceptions are related to their enactment of cognitively demanding tasks. The author found that teachers' mathematical knowledge for teaching and conceptions of teaching and learning mathematics were contingent on one another and significantly related to teachers' enactment of cognitively demanding tasks.

scholarly journals Perilaku Siswa Sekolah Dasar dalam Menyelesaikan Soal Cerita Matematika

MADRASAH ◽  
2016 ◽  
Vol 9 (1) ◽  
pp. 57
Author(s):  
Ria Norfika Yuliandari
Keyword(s):  
Word Problem ◽  
Word Problems ◽  
Teaching And Learning ◽  
Fifth Graders ◽  
Behaviour Problem ◽  
Math Model ◽  
Problem Model ◽  
Qualitative Descriptive ◽  
Thinking Process ◽  
Entrance Test

Learning word problem can be used as a means to drill students to solve problems. In word problem, students are demanded to be able to comprehend problems contexts that are given, make Math model from those problems, find ways to solve them and re-examine the results gotten. While in fact, it is shown that there are still a lot of students who find difficulties so that they make some errors in solving word problems. Related to the wills that appear to know the students’ behaviour and errors that are done by students while solving word problem by using Polya solving problem model. This study is focused to identify and classify errors that are done by students in solving word problems.. In addition, the reasons why the errors occur and hoe to solve them are going to be revealed here. This study uses qualitative descriptive approach. This research is done by students of fifth graders in SDN 1 Kebonsari Malang. The subjects of this study are chosen through the entrance test with errors variations and discussion results with teachers. There are eight students that are chosen who are divided into two students who have high ability, two students who have medium ability and four students who have low ability. Behaviour, types of errors and the reasons are gotten from the result of test and interview. The behaviour that is shown by the students of fifth graders in SDN 1 Kebonsari Malang are classified into four categories such as DTA-not proficient and DTA-proficient. Moreover, it is also found that there are other different reasons occur, but they are still related to the Pape behaviour problem solving, that is DTA-Limited Context + behaviour translation but without explanation, DTA Proficient + behaviour translation and DTA-Not Proficient + behavior translation. Based on the result of the study, it is suggested that teachers should know the errors that are often done by the students before the lesson begins to emphasize the teaching and learning process in those errors. Teachers are also able to give some practices, mainly in word problem to drill students’ experiment in solving them. Furthermore, the steps of solving the problems by using Polya model need to emphasize in terms of its usage so that it can practice students’ thinking process systematically. For the further research, if other researchers want to use this model to conduct further research so that they need to consider the application of this method in students and schools’ condition that are relatively different or other Math topics in the same subject.

scholarly journals Mathematical Knowledge for Teaching in Planning and Evaluating Instruction: What Can Preservice Teachers Learn?

2009 ◽  
Vol 40 (5) ◽  
pp. 491-529 ◽  
Author(s):  
Anne K. Morris ◽  
James Hiebert ◽  
Sandy M. Spitzer
Keyword(s):  
Preservice Teachers ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Mathematical Knowledge For Teaching ◽  
Learning Goals ◽  
Knowledge For Teaching ◽  
Mathematics Problems ◽  
Decimal Number ◽  
Starting Point ◽  
Successes And Challenges

The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an essential starting point for studying and improving one's teaching. Thirty K–8 preservice teachers completed 4 written tasks. Each task specified a learning goal and then asked the preservice teachers to complete a teaching activity with this goal in mind. For example, preservice teachers were asked to evaluate whether a student's responses to a series of mathematics problems showed understanding of decimal number addition. The results indicate that preservice teachers can identify mathematical subconcepts of learning goals in supportive contexts but do not spontaneously apply a strategy of unpacking learning goals to plan for, or evaluate, teaching and learning. Implications for preservice education are discussed.

PENERAPAN MODEL PEMBELAJARAN KOOPERATIF TIPE TEAM GAMES TOURNAMENT (TGT) UNTUK MENINGKATKAN HASIL BELAJAR IPS SISWA KELAS IVC SEKOLAH DASAR NEGERI 108 PEKANBARU

2014 ◽  
Vol 3 (1) ◽  
pp. 40
Author(s):  
Lazim. N ◽  
Zulkifli ' ◽  
Rima '
Keyword(s):  
Cooperative Learning ◽  
Social Science ◽  
Learning Outcomes ◽  
Teaching And Learning ◽  
Mathematics Learning ◽  
Average Score ◽  
Team Games ◽  
Social Science Study ◽  
Minimum Criteria ◽  
Daily Test

The problem on this research was that the low score of students’ learning on social science study. There werestill a lot of students that did not understand basic concepts and tended to memorize examples. It was showed by58,07% from 31 students achieving minimum criteria completeness (KKM) from students’ test score in IVCclass of SDN 108 Pekanbaru for Koperasi subject. The students’ average score was 62,4, and the KKM stated byschool was 68. Based on this problem it was needed to do an action research using cooperative learning modelsTeams Games Tournaments (TGT) type. This research aims to know whether the implementation of cooperativelearning models Teams Games Tournaments (TGT) type can improve students’ social science learningoutcomes at IVC class of SDN 108 Pekanbaru in 2013/2014 with 31students. This research was done in twocycles. First cycle consists of three meetings with one daily test and first tournament, and cycle II consists ofthree meetings with one daily test and second tournament. Instruments to collect data in this research areteacher’s observation sheets, students’ observation sheet, and tests. By implementing using cooperative learningmodels Teams Games Tournaments (TGT) type can improve students’ mathematics learning outcomes.Percentage of completeness in basic score was 54,8% (62,40 in average), and it changed into 77,4% (75,6 inaverage) in cycle I and 87,1% (81,1 in average) in cycle II. Percentage of teacher’ activity in cycle I was 81,9%and 92,3% in cycle II. Then percentage of students’ activity in cycle I was 75,4% and 92,2% in cycle II. Fromthose data it proves that the implementation of cooperative learning models Teams Games Tournaments (TGT)type can improve students’ learning outcomes at IVC class of SDN 108 Pekanbaru.Key Words : cooperative teaching and learning model, Teams Games Tournaments (TGT),learning outcomes

EFFECTIVENESS OF PROBLEM BASED LEARNING MODEL (PBL) SETTING OPEN ENDED APPROACH IN MATHEMATICS LEARNING

2017 ◽  
Vol 5 (3) ◽  
pp. 418
Author(s):  
Muhammad Nur Sabar
Keyword(s):  
Teaching And Learning ◽  
Hypothesis Test ◽  
Mathematics Learning ◽  
Problem Based Learning ◽  
Sampling Technique ◽  
High Category ◽  
Class Viii ◽  
The Mean ◽  
Normalized Gain ◽  
Pbl Model

The study aims at examining (1) the effectiveness of the implementation of Problem Based Learning (PBL) model using Open Ended approach, (2) the students’ learning result in mathematics who were taught by using PBL model with Open Ended approach, (3) the students’ activities in teaching and learning process by using PBL model with Open Ended approach, and (4) the students’ response on learning. The study is pre-experiment research with One Group Pretest-Posttest Design. The populations of the study were class VIII students at SMPN 33 Makassar of academic year 2016/2017 wich consisted of 10 classes. Samples were selected by employing Cluster Random Sampling technique and obtained class VIIIE as the research sample. Data were obtained by using learning result test instrument, observation sheet of students’ activities, observation sheet of learning implementation, and questionnaire of students’ response. The results of the study reveal that the learning result score of class VIII students in mathematics I sin high category, the mean 83.22, and deviation standar 8.549, the classical completeness is 87.50%, the mean of normalized gain is in high category, the students’ activity is in very active category, and students’ response on the implementation of PBL model with Open Ended approach is positive. The result of hypothesis test indicates that PBL model with Open Ended approach is effective to implemented in Mathematics learning to class VIII students at SMPN 33 Makassar. 

scholarly journals Students’ suspension of sense making in problem solving

ZDM ◽  
2021 ◽  
Author(s):  
Gemma Carotenuto ◽  
Pietro Di Martino ◽  
Marta Lemmi
Keyword(s):  
Problem Solving ◽  
Qualitative Study ◽  
Word Problem ◽  
Word Problems ◽  
Mathematical Problem ◽  
Critical Issue ◽  
Mathematical Problem Solving ◽  
Sense Making ◽  
Mathematical Problems

AbstractResearch on mathematical problem solving has a long tradition: retracing its fascinating story sheds light on its intricacies and, therefore, on its needs. When we analyze this impressive literature, a critical issue emerges clearly, namely, the presence of words and expressions having many and sometimes opposite meanings. Significant examples are the terms ‘realistic’ and ‘modeling’ associated with word problems in school. Understanding how these terms are used is important in research, because this issue relates to the design of several studies and to the interpretation of a large number of phenomena, such as the well-known phenomenon of students’ suspension of sense making when they solve mathematical problems. In order to deepen our understanding of this phenomenon, we describe a large empirical and qualitative study focused on the effects of variations in the presentation (text, picture, format) of word problems on students’ approaches to these problems. The results of our study show that the phenomenon of suspension of sense making is more precisely a phenomenon of activation of alternative kinds of sense making: the different kinds of active sense making appear to be strongly affected by the presentation of the word problem.

scholarly journals Characterizing Mathematics Learning in Colombian Higher Distance Education

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1740
Author(s):  
Elizabeth Martinez-Villarraga ◽  
Isabel Lopez-Cobo ◽  
David Becerra-Alonso ◽  
Francisco Fernández-Navarro
Keyword(s):  
Higher Education ◽  
Learning Strategies ◽  
Cultural Context ◽  
Mathematical Knowledge ◽  
Mixed Methods Research ◽  
Mathematics Learning ◽  
Sequential Design ◽  
Education Students ◽  
Approach To Learning ◽  
Conditional Knowledge

The aim of this work is to characterize the process of constructing mathematical knowledge by higher education students in a distance learning course. This was done as part of an algebra course within engineering degrees in a Colombian university. The study used a Transformative Sequential Design in mixed methods research. The analysis also determined the kinds of mathematical knowledge attained by the students and its relationship to the Colombian social and cultural context. The students acquired declarative, procedural, and conditional knowledge, while the learning strategies were often superficial. In a context where power is distant, students take on a passive approach to learning despite being highly respectful towards the educator. Thus, the educational system has the educator at the center.

A. A. Fridman. Stépéni nérazréšimosti problémy toždéstva v konéčno oprédélénnyh gruppah. Doklady Akadémii Nauk SSSR, vol. 147 (1962), pp. 805–808. - A. A. Fridman. Degrees of insolvability of the word problem in finitely defined groups. English translation of the preceding by Sue Ann Walker. Soviet mathematics, vol. 3 no. 6 (1962), pp. 1733–1737. - C. R. J. Clapham. Finitely presented groups with word problems of arbitrary degrees of insolubility. Proceedings of the London Mathematical Society, ser. 3 vol. 14 (1964), pp. 633–676. - William W. Boone. Finitely presented group whose word problem has the same degree as that of an arbitrarily given Thue system (an application of methods of Britton). Proceedings of the National Academy of Sciences, vol. 53 (1965), pp. 265–269. - William W. Boone. Word problems and recursively enumerable degrees of unsolvability. A first paper on Thue systems. Annals of mathematics, ser. 2 vol. 83 (1966), pp. 520–571. - William W. Boone. Word problems and recursively enumerable degrees of unsolvability. A sequel on finitely presented groups. Annals of mathematics, ser. 2 vol. 84 (1966), pp. 49–84.

1968 ◽  
Vol 33 (2) ◽  
pp. 296-297
Author(s):  
J. C. Shepherdson
Keyword(s):  
Word Problem ◽  
Word Problems ◽  
Nauk Sssr ◽  
London Mathematical Society ◽  
National Academy Of Sciences ◽  
Doklady Akademii Nauk Sssr ◽  
Finitely Presented Groups ◽  
Recursively Enumerable ◽  
Finitely Presented ◽  
Degrees Of Unsolvability
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