Abstract
Purpose: This study highlights the importance of teaching conceptual knowledge alongside procedural knowledge in mathematics. It examines the effects of a lack of conceptual knowledge on students’ responses to mathematics teaching from the perspectives of researchers and educators. Approach/Methodology/Design: This study draws on interviews with 30 secondary school mathematics teachers from Erbil in the Kurdistan region of Iraq on conceptual knowledge in mathematics. The study focuses on three main areas: mathematics teachers’ perspectives on teaching conceptual knowledge, the conditions needed to teach conceptual knowledge, and the obstacles that they face in teaching conceptual knowledge. Findings: A thematic analysis of the interviews revealed that mathematics teachers believed that conceptual knowledge is as important as procedural knowledge. In addition, they believed that achieving a balance between conceptual and procedural understanding and emphasizing the connections between them are necessary for understanding real mathematics. Practical Implications: Many mathematics teachers tend to use traditional teaching methods that focus on procedure and neglect conceptual mathematics. The results of this study would offer insights into the difficulties associated with mathematics teaching. Moreover, it would have practical implications for curriculum planning, emphasizing the balance of both conceptual and procedural knowledge. Originality/value: The study focuses on mathematics teachers’ perspectives on teaching mathematics conceptually, the conditions needed to teach conceptually, and the obstacles that they face in teaching mathematics conceptually.
Highlights
Over the past few decades, mathematics researchers and educators have highlighted the need to teach conceptual mathematics (Baroody & Lai, 2007; Andrew, 2019; Crooks & Alibali, 2014; Bransford et al, 2000; Clarke-Midura & Dede, 2010)
There is a relationship between conceptual knowledge and procedural knowledge; gains in conceptual knowledge lead to increases in procedural knowledge (Rittle-Johnson et al, 2001; Lauritzen, 2012; RittleJohnson & Schneider, 2015)
This study investigates the importance of conceptual teaching in addition to procedural teaching in mathematics from the perspectives of mathematics teachers in Kurdistan, to disseminate the results
Summary
Over the past few decades, mathematics researchers and educators have highlighted the need to teach conceptual mathematics (Baroody & Lai, 2007; Andrew, 2019; Crooks & Alibali, 2014; Bransford et al, 2000; Clarke-Midura & Dede, 2010). Once students gain conceptual understanding, they can assess which procedure is suitable for a specific mathematical problem (Brownell, 1945; Schneider & Stern, 2010). Many mathematics teachers tend to use traditional teaching methods that focus on procedure and neglect conceptual mathematics. Primary school mathematics teachers in Saudi Arabia (Khashan et al, 2014) relied more on procedural knowledge than conceptual knowledge. The present study examines mathematics’ teachers’ perspectives on the necessity of teaching mathematics conceptually and the obstacles that they face in this endeavor. To this end, semi-structured interviews were conducted with 30 mathematics teachers in Erbil, Iraq. The interviews were analyzed and interpreted in relation to the research questions
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