“Teaching Problem Solving in Mathematics”

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.

Teaching Students With Mild Intellectual Disability to Solve Word Problems Using Schema-Based Instruction

This study, which used a multiple baseline across students’ design, examines the effectiveness of a modified schema-based instructional approach to improve the mathematical word problem-solving performance of three students with mild intellectual disability, two of them with autism spectrum disorder. Following the intervention, the three students improved their performance when solving addition and subtraction change word problems; however, their performance was inconsistent with change word problems. The effects of the instruction were generalized to two-step addition and subtraction word problems for the three participants. Moreover, the results were generalized to an untrained setting and were maintained 8 weeks after the instruction. The implications of these findings for teaching problem-solving skills to students with intellectual disability are discussed.

Filsafat Pendidikan Politik Plato Sebagai Cara Untuk Menyiapkan Calon Pemimpin Indonesia

This study seeks to review how to formulate educational programs to prepare potential ideal leaders amid Indonesia's learning problems which are only limited to rote practice. This phenomenon results in students having little or no reasoning power. Moreover, many state officials have committed criminal acts of corruption so that students seem not to have moral role models. This teaching problem, in essence, can be prevented by Plato's philosophy of political education. This study is descriptive qualitative research. Data collection was obtained from the literature. Primary data is taken from The Republic Plato, and secondary data includes books, journals, magazines, mass media, and writings relevant to the subject matter of the discussion. From the sources that have been collected, it is then presented and then analyzed/dialogued in such a way and a conclusion is drawn. Based on the results of observations on Plato's political education philosophy, the results obtained include; the domain of discussion refers to the human soul, so in terms of education, it presupposes mousike, gymnastike, and dialectic programs. Also the allegory of the cave that Plato used to criticize the Sophists and describe the struggles of gaining knowledge. Then analyzed, and then integrated with the 2013 curriculum, resulting in educational programs: reading of Al-Barzanji text - for Muslims - or spiritual songs - for non-Muslims; martial arts; Discussion in each learning session. From there it is hoped that the ideal leader for Indonesia will emerge. Keywords: Leader, Philosophy of Political Education Plato, Education Program. Kajian ini berusaha mengulas bagaimana cara merumuskan program pendidikan untuk menyiapkan calon pemimpin ideal di tengah problematika pembelajaran Indonesia yang hanya terbatas pada praktik hafalan. Fenomena ini mengakibatkan anak didik memiliki sedikit daya nalar bahkan tidak memiliki sama sekali. Terlebih, banyak pejabat negara yang melakukan tindak pidana korupsi sehingga anak didik seperti tidak memiliki figur teladan moral. Permasalahan pengajaran tersebut, pada hakikatnya dapat dicegah dengan filsafat pendidikan politik Plato. Kajian ini merupakan penelitian kualitatif deskriptif. Pengumpulan data diperoleh dari kepustakaan. Data primer diambil dari The Republic Plato, dan data sekunder meliputi buku, jurnal, majalah, media massa, serta tulisan yang relevan dengan tajuk pembahasan. Dari sumber-sumber yang telah terkumpul, kemudian disajikan lalu dianalisis/didialogkan sedemikian rupa dan ditarik pada suatu kesimpulan. Berdasarkan hasil pengamatan terhadap filsafat pendidikan politik Plato, yang diperoleh meliputi; domain pembahasan merujuk pada jiwa manusia, sehingga dalam hal pendidikan, mengandaikan program mousike, gymnastike, dan dialektika. Juga alegori gua yang digunakan Plato untuk mengkritik kaum Sofis dan menggambarkan perjuangan saat menimba ilmu pengetahuan. Selanjutnya dianalisis, dan kemudian diintegrasikan dengan kurikulum 2013, sehingga menghasilkan program pendidikan: pembacaan teks Al-Barzanji–untuk muslim–atau lagu-lagu rohani–untuk non-muslim; pencak silat; Diskusi di setiap sesi pembelajaran. Dari sana diharapkan muncul pemimpin ideal bagi Indonesia. Kata Kunci: Pemimpin, Filsafat Pendidikan Politik Plato, Program Pendidikan.

Zjawisko niewidoczności w czasach zdalnego nauczania jako bezprecedensowy sprawdzian współodpowiedzialności w edukacji

CEL NAUKOWY: Celem rozważań jest zaprezentowanie i możliwie wieloaspektowe omówienie zjawiska uczniowskiej „niewidoczności” w czasach, gdy nauka systemowa po raz pierwszy została realizowana w formie distance teaching. PROBLEM I METODY BADAWCZE: Głównym problemem publikacji jest ujęcie i w konsekwencji zaprezentowanie wieloaspektowości zjawiska uczniowskiej „niewidoczności” w czasach zdalnego nauczania. Czynnikiem inicjującym prezentowane rozważania było doświadczenie autorki zanurzonej w konkretnym wycinku rzeczywistości edukacyjnej. Zastosowana została strategia poszukiwawcza (bazująca na analizie) wobec omawianego zagadnienia, pytań o jego istotę, specyfikę i strukturę oraz wobec odczytywania sensu i znaczenia obserwowanych zjawisk. PROCES WYWODU: We wprowadzeniu opisany został sposób komunikowania się podczas działań e‑learningowych, dzięki czemu możliwe stało się ukazanie zagadnienia komunikacyjnej nieprzejrzystości i wiążącej się z nią uczniowskiej niewidoczności. W kolejnych częściach niewidoczność ukazana została jako potrzeba, niebezpieczeństwo oraz bezprecedensowy test współczesnej edukacji, która nierzadko wypiera istnienie świadomie współodpowiedzialnego podejścia do uczenia się i nauczania. WYNIKI ANALIZY NAUKOWEJ: Finalna analiza omawianego zjawiska dość nieoczekiwanie przekierowuje odbiorcę ze zjawiska niewidoczności na problem braku uczniowskiej i nauczycielskiej współodpowiedzialności. Ten specyficzny deficyt odczuwania i poczuwania się do współodpowiedzialności przedstawiony zostaje jako główna przyczyna „niskiej noty” za zdalne nauczanie. WNIOSKI, INNOWACJE, REKOMENDACJE: Niniejsza publikacja wskazuje na konieczność pielęgnowania poczucia dydaktyczno‑wychowawczej współodpowiedzialności, której występowanie w czasach zdalnego nauczania mogłoby stać się równoważne z rozwiązaniem problemu niepożądanego zjawiska niewidoczności w czasach zdalnego nauczania.

La résolution des problèmes écrits : l’étude auprès d’une élève présentant une dyslexie

In our previous studies, we developed an approach to teaching problem-solving we termed Equilibrated Development that allows students to better understand the quantitative relationships that arise in a mathematical problem and to better choose a solution strategy. We used the method of a teaching experiment to evaluate the applicability of the developed approach to cases of students with dyslexia and to modify it, if necessary, to meet these students’ needs. Our data suggest that: a) the understanding of the mathematical structure of a problem is independent of the student's basic numerical knowledge, and b) there are conditions that allow a dyslexic student to develop mathematical reasoning to solve written problems despite difficulties in reading and writing of numbers and text.

Evaluating Learning Space Designs for Flipped and Collaborative Learning: A Transactional Distance Approach

Problem-based learning is the latest name for a teaching philosophy that is as old as Ancient Greece. Whether you call it Socratic Inquiry, case-based teaching, problem-based learning, interactive group learning, or “flipped” learning, the essential concept is to encourage the student to collaborate in applying their gained knowledge to solve a problem. As traditional lecture-based teaching has been challenged, the design of classrooms has been called into question. A flat or tiered room is not seen as an ideal setting for collaborative work. In our own College of Business, several traditional classrooms were converted to problem-based learning classrooms at considerable expense. This paper evaluates, using measures based on Michael G. Moore’s theory of transactional distance, whether moving flipped classes into these high-tech classrooms improves the collaborative learning experience. Transactional distance can be defined as the barriers that exist to a student’s engagement with their learning experience. These barriers arise due to the interaction between students and the teacher, other students, the subject matter content, and instructional technology being used. Our results suggest that, from a student engagement and outcome standpoint, the investment in costly high-tech classrooms is not warranted—a welcome result in times when university budgets are stretched to the limit.

Teaching Strategies for Mathematical Problem-Solving through the Lens of Secondary School Teachers

Many studies have been conducted on problem-solving but only a small number of studies emphasized the strategies of teaching problem-solving. This paper explores the teaching strategies for mathematical problem-solving in a secondary school in Johor, Malaysia. It involves a qualitative study in which a semi-structured interview was conducted with mathematics teachers. Data were analyzed using a sixstep thematic analysis. The results can be viewed from three contexts of findings, namely the teaching strategies, the problems faced by teachers, and the solutions to overcome the problems. The findings revealed that there are teachers who have implemented personal teaching strategies, namely the Easy-Maths Model and the Cut-Stop-Solve Model to effectively teach mathematical problem-solving. The findings also explained some problems in teaching mathematical problem-solving, whereby students’ weaknesses in basic mathematics emerged as the main drawback. This study provides useful information to teachers on the different strategies for teaching mathematical problem-solving.

Formative Assessment of Pre-Service Teachers’ Knowledge on Mathematical Modeling

This document reports how formative assessment strategies promote the knowledge of modeling of pre-service mathematics teachers. This knowledge is understood from content and vehicle points of view. Formative assessment strategies were designed and experimented with 14 participants in a mathematical modeling course offered to pre-service teachers in a Colombian university. Thematic analysis was conducted on lesson plans built by pre-service teachers. In those plans, they evinced knowledge of class management, mathematics teaching, problem solving, and modeling teaching. Finally, the collective construction of assessment rubrics is highlighted. Its contributions and limitations as a formative assessment tool are reported. The role played by the advisors’ feedback and support to pre-service teachers is also presented.