فراتحليل كيفي چارچوب هاي ارزيابي مهارت هاي طرح مسئلۀ رياضي

A Qualitative Meta-Analysis of Assessment Frameworks of Mathematical Problem-Posing Skills

اﻣﺮوزه ﻃﺮح ﻣﺴﺌﻠﻪ ﯾﮑﯽ از ﻣﻮﺿﻮﻋﺎت ﻣﻬﻢ در ﺗﺤﻘﯿﻘﺎت آﻣﻮزش رﯾﺎﺿﯽ اﺳﺖ. ﯾﮑﯽ از ﭼﺎﻟﺶﻫﺎي ﭘﮋوﻫﺸﮕﺮان ﭘﺲ از ﺑﺮرﺳﯽ ﻣﻬﺎرتﻫﺎي ﻃﺮح ﻣﺴﺌﻠﻪ و ﺑﺮرﺳﯽ ﻓﺮآﯾﻨﺪﻫﺎي ﺗﻔﮑﺮ، ﭼﮕﻮﻧﮕﯽ ارزﯾﺎﺑﯽ آﻧﻬﺎ اﺳﺖ. ﭘﮋوﻫﺶ ﺣﺎﺿﺮ ﺑﻪ ﺑﺮرﺳﯽ ﻣﺤﺘﻮا و روشﺷﻨﺎﺳﯽ اﯾﻦ ﭘﮋوﻫﺶﻫﺎ ﻣﯽﭘﺮدازد ﺗﺎ ﺳﺎﺧﺘﺎر آﻧﻬﺎ را ﻣﺸﺨﺺ ﮐﻨﺪ. اﯾﻦ ﻣﻄﺎﻟﻌﻪ، ﻓﺮاﺗﺤﻠﯿﻠﯽ ﮐﯿﻔﯽ از ﭼﺎرﭼﻮبﻫﺎي ﻋﻤﺪهاي ﮐﻪ ﭘﮋوﻫﺸﮕﺮان ﺑﺮاي ارزﯾﺎﺑﯽ ﻣﺴﺎﺋﻞ ﻃﺮح ﺷﺪه اﺳﺘﻔﺎده ﮐﺮدهاﻧﺪ، اراﺋﻪ ﻣﯽﮐﻨﺪ ﺗﺎ ﺗﺼﻮﯾﺮ ﺟﺎﻣﻌﯽ از ﺳﯿﻤﺎي اﯾﻦ ﭘﮋوﻫﺶﻫﺎ را ﻧﺸﺎن دﻫﺪ. ﺑﺮاي اﯾﻦ ﻣﻨﻈﻮر 25 ﭘﮋوﻫﺶ در ﻣﻮرد ارزﯾﺎﺑﯽ ﻣﻬﺎرتﻫﺎي ﻃﺮح ﻣﺴﺌﻠﻪ از ﺑﯿﻦ 83 ﭘﮋوﻫﺶ در ﺑﯿﻦ ﺳﺎلﻫﺎي 1994 ﺗﺎ 2020 اﻧﺘﺨﺎب و ﺗﺤﻠﯿﻞ ﺗﻮﺻﯿﻔﯽ و اﺑﺰاري ﺷﺪه اﺳﺖ. ﯾﺎﻓﺘﻪﻫﺎي ﻓﺮاﺗﺤﻠﯿﻞ 9 ﻣﻌﯿﺎر ﻣﺸﺘﺮك را در ﺑﯿﻦ ﭘﮋوﻫﺶﻫﺎ ﻣﺸﺨﺺ ﻣﯽﮐﻨﻨﺪ ﮐﻪ ﻋﺒﺎرﺗﻨﺪ از اراﺋﮥ ﯾﮏ ﺣﻞ ﺗﻮﺳﻂ داﻧﺶآﻣﻮز، ﺳﺎزﮔﺎري، ﻋﺒﺎرت رﯾﺎﺿﯽ، داﻧﺶ زﺑﺎنﺷﻨﺎﺧﺘﯽ و ﺑﯿﺎن، ﻗﺎﺑﻠﯿﺖ ﺣﻞﭘﺬﯾﺮي، ﮐﻤﯿﺖ و ﮐﯿﻔﯿﺖ دادهﻫﺎ، ﻣﺴﺎﺋﻞ ﺑﺎزﭘﺎﺳﺦ و ﻗﺎﺑﻞ ﺗﻌﻤﯿﻢ، اﺳﺘﺮاﺗﮋيﻫﺎي ﺣﻞ و راه ﺣﻞﻫﺎي ﭼﻨﺪﮔﺎﻧﻪ. ﻫﻤﭽﻨﯿﻦ ﺑﺎ ﺑﺮرﺳﯽ ﭘﮋوﻫﺶﻫﺎ ﭼﺎرﭼﻮﺑﯽ ﺷﺎﻣﻞ 11 ﻣﻌﯿﺎر و ﺑﺎ ﺗﺄﮐﯿﺪ ﺑﺮ ﻃﺮح ﻣﺴﺌﻠﻪ و ﺣﻞ ﻣﺴﺌﻠﻪ رﯾﺎﺿﯽ اراﺋﻪ ﺷﺪه اﺳﺖ. اﯾﻦ ﭼﺎرﭼﻮب ﺗﻮﺳﻂ ﻣﺘﺨﺼﺼﯿﻦ رﯾﺎﺿﯽ و آﻣﻮزش رﯾﺎﺿﯽ و ﻣﻌﻠﻤﺎن ﻫﺮ ﺳﻪ ﻣﻘﻄﻊ ﺗﺤﺼﯿﻠﯽ و ﺑﺎ ﮐﻤﮏ ﻧﻈﺮﯾﮥ ﺗﻌﻤﯿﻢﭘﺬﯾﺮي ﻣﻮرد اﻋﺘﺒﺎرﺑﺨﺸﯽ ﻗﺮار ﮔﺮﻓﺘﻪ و در دو ﻣﺮﺣﻠﻪ آزﻣﻮن ﺷﺪه اﺳﺖ.

Today, problem-Posing is one of the most important topics in mathematics education research. One of the challenges researchers face after investigating problem-posing skills and thinking processes is how to evaluate them. The present study investigates the content and methodology of these studies to determine their structure. This study presents a qualitative meta-analysis of the major frameworks that researchers have used to evaluate the posed problems in order to provide a comprehensive picture of these studies. To this purpose, 25 studies on evaluating Problem-Posing Skills were selected from 83 research studies conducted between 1994 and 2020 and analyzed descriptively and instrumentally. Students presenting a solution, adaptability, mathematical expression, linguistic knowledge and expression, solvability, quantity, and quality of data, Open-Ended and generalizable problems, solution strategies, and multiple solutions are among the nine common criteria identified by the meta-analysis findings. In addition, after reviewing the research, a framework with 11 criteria was created, with an emphasis on mathematical problem-posing and problem-solving. With the aid of generalizability theory, this framework has been validated by experts in mathematics and mathematics education, as well as teachers from all three grades, and has been evaluated in two stages.