Analysis of Middle School Mathematics Teachers' Evaluations of Skill-Based Questions within the Framework of Mathematical Competencies

Meriç Özgeldi

Makale detayları

Analysis of Middle School Mathematics Teachers' Evaluations of Skill-Based Questions within the Framework of Mathematical Competencies

Yazarlar:

Meriç Özgeldi

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Matematik Eğitimi

Dergi:

Uluslararası Türk Eğitim Bilimleri Dergisi Vol.12 Issue 1, pp.535-583

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001314762

pISSN:

2148-2314

Anahtar kelimeler:

Özet:

 The purpose of this study is to examine the solution methods developed by middle school mathematics teachers for skill-based mathematics questions and their evaluations within the framework of mathematical competencies. Mathematical competency demands are defined as communication, devising strategy, mathematizing, representation, using symbols, operations and formal language, and reasoning and argument. Thirteen middle school mathematics teachers 7 female, 6 male participated voluntarily in the study. They were asked to solve twelve skill-based questions, followed by the examination of their solutions, and then semi-structured interviews were conducted with each of them. During the interviews, the teachers were presented with semi-structured questions, and their evaluations were examined within the scope of mathematical competencies. The study results indicated that teachers apply different solutions in solving the questions and that mathematical competencies emerge at different levels within these solutions. Considering the determined levels of solutions, other competencies, except for communication competency, appeared to be at similar levels based on teachers evaluations. The competency of using symbols, operations, and formal language stood out as an essential factor in selecting among strategies. It was found that teachers could create appropriate models according to the level of demand for mathematizing competency, yet they did not evaluate the structural relationships between variables within the scope of mathematizing competency. Regarding representation competency, the most striking point was that the majority of teachers identified and used visual information. However, only a few teachers were successful in manipulating representations in a solution-appropriate manner. It was also discovered that as the demand level increases in using symbols, operations, and formal language competency, the increase in the number, type, and procedures of operations used is not always correct with these solution methods. Teachers could not identify the mathematical deductions utilized in the solution process. The majority addressed them at a lower demand level in their evaluations.

 The purpose of this study is to examine the solution methods developed by middle school mathematics teachers for skill-based mathematics questions and their evaluations within the framework of mathematical competencies. Mathematical competency demands are defined as communication, devising strategy, mathematizing, representation, using symbols, operations and formal language, and reasoning and argument. Thirteen middle school mathematics teachers 7 female, 6 male participated voluntarily in the study. They were asked to solve twelve skill-based questions, followed by the examination of their solutions, and then semi-structured interviews were conducted with each of them. During the interviews, the teachers were presented with semi-structured questions, and their evaluations were examined within the scope of mathematical competencies. The study results indicated that teachers apply different solutions in solving the questions and that mathematical competencies emerge at different levels within these solutions. Considering the determined levels of solutions, other competencies, except for communication competency, appeared to be at similar levels based on teachers evaluations. The competency of using symbols, operations, and formal language stood out as an essential factor in selecting among strategies. It was found that teachers could create appropriate models according to the level of demand for mathematizing competency, yet they did not evaluate the structural relationships between variables within the scope of mathematizing competency. Regarding representation competency, the most striking point was that the majority of teachers identified and used visual information. However, only a few teachers were successful in manipulating representations in a solution-appropriate manner. It was also discovered that as the demand level increases in using symbols, operations, and formal language competency, the increase in the number, type, and procedures of operations used is not always correct with these solution methods. Teachers could not identify the mathematical deductions utilized in the solution process. The majority addressed them at a lower demand level in their evaluations.

 The purpose of this study is to examine the solution methods developed by middle school mathematics teachers for skill-based mathematics questions and their evaluations within the framework of mathematical competencies. Mathematical competency demands are defined as communication, devising strategy, mathematizing, representation, using symbols, operations and formal language, and reasoning and argument. Thirteen middle school mathematics teachers 7 female, 6 male participated voluntarily in the study. They were asked to solve twelve skill-based questions, followed by the examination of their solutions, and then semi-structured interviews were conducted with each of them. During the interviews, the teachers were presented with semi-structured questions, and their evaluations were examined within the scope of mathematical competencies. The study results indicated that teachers apply different solutions in solving the questions and that mathematical competencies emerge at different levels within these solutions. Considering the determined levels of solutions, other competencies, except for communication competency, appeared to be at similar levels based on teachers evaluations. The competency of using symbols, operations, and formal language stood out as an essential factor in selecting among strategies. It was found that teachers could create appropriate models according to the level of demand for mathematizing competency, yet they did not evaluate the structural relationships between variables within the scope of mathematizing competency. Regarding representation competency, the most striking point was that the majority of teachers identified and used visual information. However, only a few teachers were successful in manipulating representations in a solution-appropriate manner. It was also discovered that as the demand level increases in using symbols, operations, and formal language competency, the increase in the number, type, and procedures of operations used is not always correct with these solution methods. Teachers could not identify the mathematical deductions utilized in the solution process. The majority addressed them at a lower demand level in their evaluations.

 Bu çalışmanın amacı, ortaokul matematik öğretmenlerinin beceri temelli matematik soruları için geliştirdikleri çözüm yöntemlerinin ve bu çözümler kapsamında yaptıkları değerlendirmelerinin matematiksel yetkinlikler çerçevesinde incelenmesidir. Matematiksel yetkinlik talepleri iletişim, strateji geliştirme, matematikleştirme, temsil, sembolleri, işlemleri ve resmi dili kullanma, akıl yürütme ve argüman geliştirme olarak tanımlanmaktadır. Çalışmaya 13 ortaokul matematik öğretmeni 7 Kadın, 6 Erkek gönüllü olarak katılmıştır. Çalışmaya katılan öğretmenlere 12 beceri temelli soru sorulmuş, öğretmenlerin çözümleri incelenmiş ve ardından her biri ile yarı yapılandırılmış görüşmeler düzenlenmiştir. Görüşmelerde öğretmenlere yarı-yapılandırılmış sorular sorulmuş ve yaptıkları değerlendirmeler matematiksel yetkinlikler kapsamında incelenmiştir. Çalışmanın sonuçları, öğretmenlerin soruların çözümlerinde farklı çözümler uyguladıkları ve bu çözümler kapsamında matematiksel yetkinliklerin farklı düzeylerde ortaya çıktığını göstermektedir. Çözümlerin belirlenen düzeyleri göz önünde bulundurulduğunda, öğretmenlerin değerlendirmelerine göre iletişim yetkinliği dışında diğer yetkinliklerin belirlenen seviyeleri benzerdir. Stratejiler arasında seçim yapma eyleminin gerçekleştirilmesinde önemli etken olarak çözüm sürecinde sembolleri, işlemleri ve resmi dili kullanma yetkinliği öne çıkmaktadır. Öğretmenlerin matematikleştirme yetkinliğinin talep düzeyine uygun olan modellemeler oluşturabildikleri; fakat değişkenler arasındaki yapısal ilişkileri matematikleştirme yetkinliği dâhilinde değerlendirmedikleri görülmüştür. Temsil yetkinliği kapsamında en dikkat çeken nokta, öğretmenlerin çoğunun görsel bilgileri belirleyip kullanmaları, ancak temsilleri çözüme uygun şekilde manipüle etmekte az sayıda öğretmenin başarılı olmasıdır. Sembolleri, işlemleri ve resmi dili kullanma yetkinliğinde talep düzeyi arttıkça kullanılan işlem sayısı, türü ve prosedürlerin artmasının her durumda doğru olmadığı bu çözüm yöntemleriyle görülmüştür. Öğretmenlerin genellikle çözüm sürecinde kullanılan matematiksel çıkarımları belirleyemedikleri ve çoğunluğunun değerlendirmelerinde daha düşük talep düzeyinde ele aldıkları görülmüştür.

Makale detayları

Analysis of Middle School Mathematics Teachers' Evaluations of Skill-Based Questions within the Framework of Mathematical Competencies

Yazarlar:

Meriç Özgeldi

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Matematik Eğitimi

Dergi:

Uluslararası Türk Eğitim Bilimleri Dergisi Vol.12 Issue 1, pp.535-583

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001314762

pISSN:

2148-2314

Mathematical Competency

Skill-Based Questions

Mathematics TeacherMatematiksel Yetkinlik

Beceri Temelli Sorular

Matematik Öğretmeni

Sayı

Makale detayları

Analysis of Middle School Mathematics Teachers' Evaluations of Skill-Based Questions within the Framework of Mathematical Competencies

Yazarlar: Meriç Özgeldi

Yayıncı: Tokat Gaziosmanpasa University

Ana Başlıklar: Matematik Eğitimi

Dergi: Uluslararası Türk Eğitim Bilimleri Dergisi Vol.12 Issue 1, pp.535-583

Belge Tipi: Makale

Yayın Tarihi: 3/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001314762

pISSN: 2148-2314

Mathematical Competency

Skill-Based Questions

Mathematics TeacherMatematiksel Yetkinlik

Beceri Temelli Sorular

Matematik Öğretmeni

Sayı

Yazarlar:

Meriç Özgeldi

Yayıncı:

Tokat Gaziosmanpasa University

Ana Başlıklar:

Matematik Eğitimi

Dergi:

Uluslararası Türk Eğitim Bilimleri Dergisi Vol.12 Issue 1, pp.535-583

Belge Tipi:

Makale

Yayın Tarihi:

3/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001314762

pISSN:

2148-2314