Reasoning and Problem Solving/Putting the Theories to Work: The Case of Mathematics
Chapter 4 – Information Processing, Memory, and Problem Solving
Reasoning and Problem Solving
Reasoning is thinking directed toward reaching a goal, while problem solving is a means of reaching that goal. Problem solving is the ability to reason. Reasoning builds on generalization and inference to process new information into useable data that can be used for problem solving. In the educational setting, strategies taught in textbooks are usually contrived for the solutions presented in contrast to real world problems that may be more complex and require advanced thinking solutions (Bergin & Bergin, 2012).
Children learn in a predictable manner and begin at birth using generalization to solve problems. Toddlers begin to compare and contrast concepts in order to generate abstract rules. By pre-school age most children have developed enough reasoning ability to use evidence to draw conclusions based on previous experience. This reasoning can be cultivated through training, but at this stage is not flawless. By middle childhood most students have a well developed internal speech for problem solving. Children at this age begin to try new strategies when one that had previously worked has failed.
By adolescence, children think much like adults and can draw conclusions based on numerous variables. Diversity amongst individuals when it comes to reasoning ability is based on many things. Genetics, education and experience, and modeling are key concepts in reasoning ability and problem solving. Student working memory and processing speed are likely beyond the educator’s control, but teacher feedback allows students to revise their strategies in order to find out what works (Malamed, 2013). Questions such as, “How do you know that?” or “Why is that answer right?” allow the student to verbalize their reasoning and allow the teacher to help the student codify their thinking.
Putting the Theories to Work: The Case of Mathematics
While “number sense” is likely innate, mathematical competence in areas such as percentages, algebra or fractions must be taught, and learned. Informal math concepts prevalent in infants and toddlers are acquired without formal training. The math skill possessed by a child at entrance into kindergarten is a likely predictor of academic success, even more so than reading skill. Children of lower economic status may not have developed the elementary math skills needed as a foundation for success (Purcell-Gates, 1995). The ability to memorize math concepts such as the multiplication tables allows the student to quickly move from rudimentary calculations to more advanced math.
The textbook describes four perspectives to explain math ability. Behaviorism believes in direct instruction involving drill and practice in order to learn basic lower level skills and then build on these concepts. According to Piaget, children assimilate what they know into new strategies based on previous experience. Diagrams, graphs and asking the student to explain their answers are frequent strategies of instruction. Vygotsky believed that knowledge is transmitted through social and cultural means and then transferred to other areas. Cooperative learning were children talk about problem solving and opportunities to observe math concepts in the community are concepts for learning.
The information processing model relates that working memory and long-term memory combine for reasoning ability. Executive function keeps the student moving through right steps for solving a problem. Testing is thought to facilitate learning because of forced recall. Spaced practice allows the child to move concepts from short-term to long-term memory and back again for working out the problem. Children likely use learned strategies to become more efficient at solving problems. The information processing model allows for concepts from other theories to be seen as valid on their own without discounting the whole theory (Page & Page, 2011).
1. How do reasoning and problem solving contribute to each other?
2. Why is it important for students to verbalize their responses?
3. Why would math competence be a better indicator of future academic success than reading ability?
4. Have you considered using frequent quizzes with explanations required that build on past learning and cumulate in a larger comprehensive test?
5. Why is no single learning theory completely accurate?
Bergin, C., & Bergin, D. (2012). Child and adolescent development in your classroom. Belmont: Wadsworth.
Malamed, C. (2013). 20 facts you should know about working memory. Retrieved from
Page, R., & Page, T. (2011). Promoting health and emotional well-being in your classroom. (5th ed.). Sudbury: Jones and Bartlett Publishers.
Purcell-Gates, V. (1995). Other people’s words: The cycle of low literacy. Cambridge: Harvard University Press.