Emotional blocks are the things that we feel that stop us to problem solve accurately. This could be not suggesting an idea because it may sound stupid, and make us appear silly. Another example, is fear of change, or feeling guilty that the problem occurred in the first place. Intellectual blocks – Intellectual barriers can be caused by not having the training, skills or knowledge to solve a problem. For example, it could be a lack of skills in evaluation or research etc.
Teaching and learning strategies to enhance problem solving: Many instructors in engineering, math and science have students solve “problems”. But are their students solving true problems or mere exercises? The former stresses critical thinking and decision making skills whereas the latter requires only the application of previously learned procedures. True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.
Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.
Principles for teaching problem solving: Model a useful problem-solving method. Problem solving can be difficult and sometimes tedious. Show students by your example how to be patient and persistent and how to follow a structured method, such as Woods’ model described here. Articulate your method as you use it so students see the connections.
Teach within a specific context. Teach problem-solving skills in the context in which they will be used (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
Help students understand the problem. In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
Take enough time. When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal, both individually and as a class; dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
Ask questions and make suggestions. Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
Link errors to misconceptions: Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.
Teaching mathematics to children can be extremely challenging, especially when it comes to problem solving. This is when students really have a hard time. Problem-solving tools are the key to enhance the problem-solving proficiency in students. Using teaching strategies to get students to use the right solving formats is just as important as getting them to get the correct answer. Teach students that there is more than one way to get an answer, and this will help them to expand their thinking. Here, are the teaching strategies that your students need in order to help improve their math problem-solving skills.
This strategy involves deciding which mathematical operation students will use (addition, subtraction, multiplication, division, or a combination of operations). When choosing a mathematical operation, students will need the ability to understand the literal meaning of the sentence, as well as understand how to express the meaning mathematically. In other words, in order to successfully find a solution to the problem, students will need both their reading and mathematical skills.
Understanding how to choose an operation can be difficult for many students, especially for students who struggle with reading. The easiest way to teach students how to choose an operation is to teach them to identify key words. Consider writing this chart below on your front board and have students copy it into their problem solving notebooks.
The two strategies listed above are just two problem-solving strategies students can use. There are many, many more. In order for students to become great problem solvers, it is suggested that students keep a problem-solving notebook. In this notebook students should keep important information that they can refer to, like the “Key words” mentioned earlier, as well as these tips:
Read the problem carefully.
Cross out any unnecessary information that is not relevant.
Think about what strategy you want to use.
Make sure that the strategy makes sense.
Read the problem once through and decide if that is the strategy you want to use.
Draw a picture or use manipulatives to help you solve the problem.
Emotional blocks are the things that we feel that stop us to problem solve accurately. This could be not suggesting an idea because it may sound stupid, and make us appear silly. Another example, is fear of change, or feeling guilty that the problem occurred in the first place. Intellectual blocks – Intellectual barriers can be caused by not having the training, skills or knowledge to solve a problem. For example, it could be a lack of skills in evaluation or research etc.
Teaching and learning strategies to enhance problem solving: Many instructors in engineering, math and science have students solve “problems”. But are their students solving true problems or mere exercises? The former stresses critical thinking and decision making skills whereas the latter requires only the application of previously learned procedures. True problem solving is the process of applying a method – not known in advance – to a problem that is subject to a specific set of conditions and that the problem solver has not seen before, in order to obtain a satisfactory solution.
Below you will find some basic principles for teaching problem solving and one model to implement in your classroom teaching.
Principles for teaching problem solving: Model a useful problem-solving method. Problem solving can be difficult and sometimes tedious. Show students by your example how to be patient and persistent and how to follow a structured method, such as Woods’ model described here. Articulate your method as you use it so students see the connections.
Teach within a specific context. Teach problem-solving skills in the context in which they will be used (e.g., mole fraction calculations in a chemistry course). Use real-life problems in explanations, examples, and exams. Do not teach problem solving as an independent, abstract skill.
Help students understand the problem. In order to solve problems, students need to define the end goal. This step is crucial to successful learning of problem-solving skills. If you succeed at helping students answer the questions “what?” and “why?”, finding the answer to “how?” will be easier.
Take enough time. When planning a lecture/tutorial, budget enough time for: understanding the problem and defining the goal, both individually and as a class; dealing with questions from you and your students; making, finding, and fixing mistakes; and solving entire problems in a single session.
Ask questions and make suggestions. Ask students to predict “what would happen if …” or explain why something happened. This will help them to develop analytical and deductive thinking skills. Also, ask questions and make suggestions about strategies to encourage students to reflect on the problem-solving strategies that they use.
Link errors to misconceptions: Use errors as evidence of misconceptions, not carelessness or random guessing. Make an effort to isolate the misconception and correct it, then teach students to do this by themselves. We can all learn from mistakes.
Teaching mathematics to children can be extremely challenging, especially when it comes to problem solving. This is when students really have a hard time. Problem-solving tools are the key to enhance the problem-solving proficiency in students. Using teaching strategies to get students to use the right solving formats is just as important as getting them to get the correct answer. Teach students that there is more than one way to get an answer, and this will help them to expand their thinking. Here, are the teaching strategies that your students need in order to help improve their math problem-solving skills.
This strategy involves deciding which mathematical operation students will use (addition, subtraction, multiplication, division, or a combination of operations). When choosing a mathematical operation, students will need the ability to understand the literal meaning of the sentence, as well as understand how to express the meaning mathematically. In other words, in order to successfully find a solution to the problem, students will need both their reading and mathematical skills.
Understanding how to choose an operation can be difficult for many students, especially for students who struggle with reading. The easiest way to teach students how to choose an operation is to teach them to identify key words. Consider writing this chart below on your front board and have students copy it into their problem solving notebooks.
The two strategies listed above are just two problem-solving strategies students can use. There are many, many more. In order for students to become great problem solvers, it is suggested that students keep a problem-solving notebook. In this notebook students should keep important information that they can refer to, like the “Key words” mentioned earlier, as well as these tips: