Virtually all levels of mathematics depend on problem solving skills. Learning to solve problems involves:
- actively investigating and exploring math concepts within a word problem or math activity
- applying previously learned information to new and different situations
- forming pictures in one’s mind to represent math concepts and visualize word problems
- applying the process of estimation to solving math problems
- establishing the reasonableness of a math solution
Effective math problem solving requires students to be both systematic in their approach to problems and flexible in their use of strategies.
Throughout the process of mathematical development, students are expected to operate on an increasingly abstract symbolic level. Areas of higher math, such as probability, statistics, geometry and algebra, require students to apply logical reasoning skills which are both sequential (as in multi-step equations) and spatial (as in geometric relationships).
This chart describes important skills related to math problem solving and higher math.
|Necessary SubSkills||Common Obstacles||Helpful Tips|
|Student can use mental imagery to conceptualize math activities and can create picture of a math word problem in his mind||Student has difficulty using mental pictures (such as patterns or shapes) to represent math concepts, or has difficulty “seeing” the math problem in his/her mind.||view|
|Student understands math word problems he/she reads, even when irrelevant information is given, or when information is given in an order different from the order of the computation.||Student is confused by the language of word problems, such as when irrelevant information is included or when information is given out of sequence||view|
|Student has a systematic way of approaching math problems, and is able to break complex problems down into manageable steps.||Student doesn’t know how to get started on word problems, or how to break problems down into simpler subproblems||view|
|Student is able to actively think through a problem, employing techniques such as applying known strategies to novel problems or adjusting strategies while working through a problem||Student has difficulty reasoning through a problem, or difficulty using strategies effectively during problem solving||view|
|Student works on a developmentally appropriate level in areas of higher math, such as algebra, geometry, and statistics||Student has difficulty in grade level areas of higher math, such as algebra, geometry, or statistics||view|