This chapter did not present many new ideas to me, although I truly value students working with context or story problems. The key ideas of looking for patterns, using visual models, communication, using self questioning, and being able to explain the problem are all things that we currently encourage. I do believe we do not insist on perseverance enough and do not aim high enough on clarity of the explanation of the problem solving. I did find it interesting about not focusing on key words because it encourages a short cut that does not always work and having it discourage the true goal of analyzing or truly understanding what the problem is trying to solve. Chapter three usefulness certainly overshadows this chapter for me.
The key word strategy refers to teaching students to look for for a 'key word' in word problems that may suggest which action to take (addition, subtraction, multiplication, division). This technique has been taught often by teachers and textbooks reinforce this idea by creating simplistic word problems. However, there are 4 arguments against using key word strategies... 1. it sends the wrong message about doing math (students use the easy way out) 2. keys words can be misleading 3. problems may not have key words 4. key words don't work with two-step or more advanced problems.
A great example in the book is the problem 'There are three boxes of chicken nuggets on the table. Each box contains six chicken nuggets. How many chicken nuggets are there in all?' Students often referred to the words 'how many in all' and concluded that 3 + 6 = 9 versus analyzing the problem to conclude that multiplication should be used.
I didn't know how to interpret this question, but Tiffany's response certainly makes sense. For Compare addition and subtraction problems, for example, the term "more" can cause confusion. Generalizing that 'addition' means 'more' and 'subtraction' means 'less' may cause confusion when students are working with word problems. This confusion can be further compounded when working with the properties of zero. From p. 178, "children believe that 6 + 0 must be more than 6 because 'adding makes numbers bigger,' or that 12 - 0 must be 11 because 'subtraction makes numbers smaller.'"
When first approaching this question, though, I was thinking more broadly, The use of key words may create unintended boundaries for students when solving problems. These boundaries may in turn pigeonhole students into a single strategy to solve a given problem rather than encouraging them to think flexibly to solve a problem. For example, for addition and subtraction examples of Figure 9.1, "the problems are described in terms of their structure and interpretation and not as addition or subtraction problems" (p. 169). Similarly, with the properties of zero, "explicit attention to these concepts (build the terminology over time) will help students become more flexible (and efficient) in how they combine numbers" (p. 178).
Is there similar confusion with multiplication and division - 'groups of' and 'sets of'? Because multiplication is commutative, does it make sense to emphasis this terminology? The important thing is that the student can tell you what each factor in their equations and explanation represents.
Addition is commutative too! I think you are right on, Dean, and I would think of this more broadly as well. Using keywords to solve problems with negative numbers in it might be tricky, especially if you are asked to subtract a negative. (-3 - -7= ?) Keywords would lead students astray with these kinds of questions. This chapter makes me think of studying for the Praxis Exam, and how the test book is full of advice like this. This is how to retain and learn things for the short-term to pass a test, but nothing that alone will build knowledge and number sense. Students need to realize the whole problem, not just keywords.
I agree with Katherine in her response as to how key words can be used as a crutch for some students and a distraction for other students learning math concepts. Key words seem to take away the high level thinking or struggle that comes with sitting with the problem and trying to understand what the question is, how it looks visually and what algorithum would be best suited. I wonder what taking the key word out of word problems would look like for the 5th. I will have to try.
Katherine you just summed everything up so well! I know as a student who struggled with math my whole life I was looking for shortcuts to help me understand. I would remember the method we were learning and just use that to complete the work. It worked fine sometimes on on tests that reviewed a variety of material (like the end of the year or semester) I never really knew what they were asking and was often at a loss for what methods I was supposed to use. I could have definitely used some more instruction on the process of what I was doing to help make sense of it all.
This chapter did not present many new ideas to me, although I truly value students working with context or story problems. The key ideas of looking for patterns, using visual models, communication, using self questioning, and being able to explain the problem are all things that we currently encourage. I do believe we do not insist on perseverance enough and do not aim high enough on clarity of the explanation of the problem solving. I did find it interesting about not focusing on key words because it encourages a short cut that does not always work and having it discourage the true goal of analyzing or truly understanding what the problem is trying to solve. Chapter three usefulness certainly overshadows this chapter for me.
ReplyDeleteThe key word strategy refers to teaching students to look for for a 'key word' in word problems that may suggest which action to take (addition, subtraction, multiplication, division). This technique has been taught often by teachers and textbooks reinforce this idea by creating simplistic word problems. However, there are 4 arguments against using key word strategies... 1. it sends the wrong message about doing math (students use the easy way out) 2. keys words can be misleading 3. problems may not have key words 4. key words don't work with two-step or more advanced problems.
ReplyDeleteA great example in the book is the problem 'There are three boxes of chicken nuggets on the table. Each box contains six chicken nuggets. How many chicken nuggets are there in all?' Students often referred to the words 'how many in all' and concluded that 3 + 6 = 9 versus analyzing the problem to conclude that multiplication should be used.
I didn't know how to interpret this question, but Tiffany's response certainly makes sense. For Compare addition and subtraction problems, for example, the term "more" can cause confusion. Generalizing that 'addition' means 'more' and 'subtraction' means 'less' may cause confusion when students are working with word problems. This confusion can be further compounded when working with the properties of zero. From p. 178, "children believe that 6 + 0 must be more than 6 because 'adding makes numbers bigger,' or that 12 - 0 must be 11 because 'subtraction makes numbers smaller.'"
DeleteWhen first approaching this question, though, I was thinking more broadly, The use of key words may create unintended boundaries for students when solving problems. These boundaries may in turn pigeonhole students into a single strategy to solve a given problem rather than encouraging them to think flexibly to solve a problem. For example, for addition and subtraction examples of Figure 9.1, "the problems are described in terms of their structure and interpretation and not as addition or subtraction problems" (p. 169). Similarly, with the properties of zero, "explicit attention to these concepts (build the terminology over time) will help students become more flexible (and efficient) in how they combine numbers" (p. 178).
Is there similar confusion with multiplication and division - 'groups of' and 'sets of'? Because multiplication is commutative, does it make sense to emphasis this terminology? The important thing is that the student can tell you what each factor in their equations and explanation represents.
Addition is commutative too!
DeleteI think you are right on, Dean, and I would think of this more broadly as well.
Using keywords to solve problems with negative numbers in it might be tricky, especially if you are asked to subtract a negative. (-3 - -7= ?) Keywords would lead students astray with these kinds of questions.
This chapter makes me think of studying for the Praxis Exam, and how the test book is full of advice like this. This is how to retain and learn things for the short-term to pass a test, but nothing that alone will build knowledge and number sense. Students need to realize the whole problem, not just keywords.
I agree with Katherine in her response as to how key words can be used as a crutch for some students and a distraction for other students learning math concepts. Key words seem to take away the high level thinking or struggle that comes with sitting with the problem and trying to understand what the question is, how it looks visually and what algorithum would be best suited. I wonder what taking the key word out of word problems would look like for the 5th. I will have to try.
DeleteThe unknown reply above is mine. :-)
DeleteKatherine you just summed everything up so well! I know as a student who struggled with math my whole life I was looking for shortcuts to help me understand. I would remember the method we were learning and just use that to complete the work. It worked fine sometimes on on tests that reviewed a variety of material (like the end of the year or semester) I never really knew what they were asking and was often at a loss for what methods I was supposed to use. I could have definitely used some more instruction on the process of what I was doing to help make sense of it all.
Delete