![\"\"](\"http:\/\/bookunitsteacher.com\/flipchart\/math\/problemsolving\/anchorchart.jpg\")
One of the “keyword” anchor charts that lurk on Pinterest<\/p><\/div>\n
I’ll show\u00a0with just how bad an idea it is to teach problem solving with keywords by using\u00a0a single example:\u00a0I had 5\u00a0apples in my basket on Monday. On Tuesday I increased the amount of\u00a0apples so now I have 7\u00a0altogether. How many apples did I add on Tuesday?<\/em><\/p>\n If the student had been the victim of a teacher who used the “key word” approach, then by following these directions, he would have been absolutely correct to add 5\u00a0and 7\u00a0to get 12\u00a0apples. After all, the “key word” altogether<\/em> is used in the question, as well as increased\u00a0<\/em>and\u00a0added.<\/em>\u00a0The question does not contain any of the subtraction keywords, which includes\u00a0difference, take away, left, still, minus\u00a0<\/em>and\u00a0take away<\/em>.<\/p>\n Some teachers might argue that this is a “gotcha” question, but this is not the case. In fact, it is a question that I would hope a 3rd grader who has a grade-level understanding of English would be able to turn into an equation and solve. The “key word” technique\u00a0is a kind of hunt & peck approach to reading and interpreting word problems, and it results in students performing the wrong operation on anything but the most obvious problems. Am I crazy, or is this a seriously bad way to teach problem solving?<\/p>\n So what should we be doing in the classroom instead of teaching “key words?” The best approach is to do things that actually require thinking, like having the students build models that will help them solve the problem. Mathematicians do this all the time; why not have students? These models could be physical or written, but regardless, they are models and they help students actually “think” about the meaning of a problem.<\/p>\n The second model does essentially the same thing, but uses manipulatives: the child “acts out” the timeline of the problem by putting 5 beans in the first circle, showing that some apples are being added, and the result is 7.<\/p>\n Please, please don’t download or hang this chart in your classroom.<\/p><\/div>\n I don’t know who came up with the idea for using “key words” when teaching children about problem solving. It’s a seriously bad idea that somehow made its into the everyday practice of misguided teachers around everywhere. It substitutes comprehension for shortcuts, and disengages children from the actual practice of what mathematical thinking look like. I can guarantee you that there is not<\/span> a single economist, biologist, chemist, statistician or anybody working in the field of mathematics who solves a problem using this method. Why would we teach it to our students?<\/p>\n <\/p>\n <\/p>\n Note: this rant has been brought to you by none other than Robert M. Berkman, proprietor of the SamizdatMath<\/a>\u00a0curriculum collective. If you are interested in including visual approaches to problem solving, try out this set of algebra problems which promote algebraic reasoning without<\/span> the use of nonsensical “key words!” I work with a student who attends a school for children with special needs. He’s a very nice kid who is very eager to do well in math, even though it presents many challenges to him. His parents decided to … Continue reading ![\"model2\"](\"http:\/\/bltm.com\/blog\/wp-content\/uploads\/2015\/01\/model2-300x192.jpg\")
![\"model1\"](\"http:\/\/bltm.com\/blog\/wp-content\/uploads\/2015\/01\/model1-300x157.jpg\")
Both models to the right can be used to solve the problem described above. The top one uses a “bar model” which is attributed to the Singapore Math program, but was actually developed by W.W. Sawyer<\/a> over a half-century ago. By comparing the part (the 5 apples I had on Monday) with the whole (the 7 apples I now have on Tuesday), I understand that I am “adding” on to 5 until I get to 7.<\/p>\n![\"\"](\"http:\/\/media-cache-ec0.pinimg.com\/736x\/fa\/7f\/71\/fa7f71a173039f00a6a71090ee8fa6ac.jpg\")
![\"\"](\"https:\/\/datax.teacherspayteachers.com\/thumbitem\/Beans-in-a-Pan-Algebra-Puzzles-for-Elementary-and-MIddle-Schoolers\/original-197778-1.jpg\")
<\/a><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"