numberless word problems kaplinsky
If I can frame my questions to match their experience, they understand much better. Interesting wonders April. For example, let’s say your original problem is: “Damian has 6 cars and then his mom gives him 4 more. They will use the 2 numbers for the numbers needed in the problem. This way children can start to form the story in their heads without worrying about the numbers. While not ideal, personally I believe that in real life, the kids will be fine if they have conceptual understanding but forget the vocabulary. One thing I have wondered about the confusion between perimeter and area and whether we have added to the confusion is the use of using one-dimensional units when we talk about buying flooring for example. We tend to think that teaching two confusing concepts together and asking kids to repeatedly discern between them. Thanks Jeremy. We decided as a class that were at least two ways we could think of to measure size (the tiling of the inside and the ribbon of the outside) – and then there was a need for vocabulary. How many markers did Gina buy?” You may see this problem as 50 – 15 = 35. Based on my experiences, this seems to be a pretty typical outcome for all math educators. area.) Sometimes when we’ve translated to a word problem, a lot of the authenticity goes away. Hi Connie. Have you seen Robert Kaplinsky’s Shepard Problem video? Each time the skeptics said they were not completely convinced. One of my favorite problem solving activities is a numberless word problem sort. Then they will roll the dice. What if??? Manipulatives and/or good computer graphics, and/or really good illustrations strike me as fundamental for many students. Students would not be assessed on the terms, but their interest may be piqued in a natural way and they could choose or not choose to use the historical math term during discourse about such problems. Great point Ian. Thanks for your perspective. It happened every year. While teaching students that the area refers to the flat surface, while the perimeter is talking about the outer edge, this negates the fact that both area and perimeter are measurements….not locations! There are som. While I agree with you that context is so very important in having students “understand” that which we are asking them to do/solve, I also think that a lot of teachers (who are obviously adults) fail to understand that “context” for them is different from “context” for a young student. Later in the year, perimeter is introduced as an extension of length. I do see your point Caroline, but this is a very I think that this is a very tricky situation. Most of my students struggle with reading and language as well, so I’ve often thought it was a vocabulary issue. Check out this problem from Graham Fletcher: https://gfletchy.com/packing-sugar/. Success! This helps they to develop their own definition after having multiple exposures if seeing, hearing and using the word while solving problems throughout the unit. Expecting them to “get it” in any meaningful way from a one-size-fits-all approach, particularly one that is highly abstract, is a guarantee that many will be left in the dust. In his study, 75% of students answered incorrectly. Regardless of the sequence, the fact remains that our students are constantly searching for the shortcut. We made duplicates of our shapes for them to play with and they began to explore. This isn’t great but it’s the first one that pops into my head. Or, is it better to give them the vocabulary first and teach them what it means? Confusion seemed much less this year and truthfully we all had more fun. So, i think we should aim to find a balance where students begin with the context, realize that it is burdensome to always have the context, and then abstract it so that they can focus more on efficiency. Or have never stepped into a fenced bball court? The unnecessary facts can even be silly. For example, if you ask a student to find the perimeter of a rectangle, they will often give you the rectangle’s area. Did I do a better job explaining myself this time? Would they develop a model that avoids the possibility of incorrectly double/single counting corners? Problems that allow for multiple entry points, student discovery and are grounded in real world scenarios are ones that will allow for mastery of skills and retention. For example, multiplication of two and three-digit numbers can be demonstrated with a rectangular area model before teaching the algorithm. Composite figures also provide interesting insight into what students already know about area and perimeter. I am less concerned with having the proper vocabulary than most, perhaps. So while they may not necessarily name it themselves, they realize that it is something that needs to be properly defined. If you’ve ever taught students how to find the area or perimeter of a shape, you won’t be surprised to read that students commonly confuse the two measurements. Open ended discussions and explorations take a lot of time. In any of these cases, there’s really no thinking about what it means to find area or perimeter, so any calculation is as good as another. Hmm. There was an error submitting your subscription. Robert Kaplinsky. One of the things I do for perimeter and area is to talk about our school garden and building planters. How many meters did he run? Actually, I think the real problem is teaching them too close together. A rectangle with dimensions identified could be used to find both the area and perimeter, which gives students at best a 50-50 chance. Tips for making this strategy work: This strategy is perfect for tricky numbers like fractions or numbers in scientific notation. For the longest time I couldn’t figure out why students couldn’t get the difference between pronouns and proper nouns. I think it would go like this though: 1. Well, I agree; however, we still need to test vocabulary knowledge. So exciting to see the success that kindergarten students are having with numberless word problems and notice/wonder! 2. Talk about why you are putting each number where it goes as you write it. They came up with many different ideas on how to prove how big each shape was – one group tiled but not very neatly, one group tiled but didn’t cover the entire shape, one group made a tile line that measured the length and width of the longest point of each shape, one group placed pairs of tiles all over the shape being careful not to go over the lines. How do you de-abstract my question? This often means that they will never keep the two concepts straight. Subscribe and receive access to our library of FREE printables and never miss a post. Imagine asking students something like, “How many sugar cubes are inside the box? I think the important thing is finding the balance between context and abstraction. For instance, Jeremy was one minute late for basketball practice and had to run a lap. I am less concerned about when they are taught this than I am that they come from an authentic context and are derived from there. It was amazing. . Or for some, it might be that adding together any two numbers is their go-to strategy, so the addition part of perimeter sticks, but the multiplication part 2(l + w) goes out the window, and they miss that this is the same as 2l + 2w because math is really just a bunch of meaningless symbols (David Hilbert sort of said the same thing, though I don’t think he meant “meaningless” in the same way students do). Often, when presented with abstract concepts, they will shut down until I connect the abstract concept to something that is familiar to them. I’m not sure if anyone has experimented with this, but exploring one concept, separated by some months from another, might alleviate the confusion. At what point do we just have to assign some terminology and set about memorizing which terms go with which concepts? What do we give up if we devote all the time needed to cementing the conceptual understanding and matching terminology of both concepts? Enter your email address to follow this blog and receive notifications of new posts by email. Plus, it is fun. In addition, students themselves need to repeatedly use the terms so that it becomes part of the classroom conversation. To draw a picture requires a student to think about what the problem says. Students may not have any experiences with a fenced backyard. copyright © 2019 Randi Smith All Rights Reserved. What if the problem’s context was less fake and more useful? You could also follow-up by placing the numbers in part-part-whole circles, especially if you are not sure your child is understanding how the numbers relate to each other well. So I wonder how many students connect to turf and fences? For example, 3 x 5 can be represented as: The idea of teaching a concept when it’s relevant would be a tricky rule to enforce, but I do understand where you’re coming from. I know this post doesn’t do the justice and thinking that Brian has in his posts but I will post more as I go through them. Then, the students’ task is to read the story and write 2-3 math questions that can be answered. So for the above problem, you might say: “Gina had 15 markers so we will write that number first. Getting students to break this habit is no easy task. We can put the problem into context but the units of measurement might still be very abstract for them. True, I am over 30 and the way I remember being taught perimeter, area and volume was to visualize a drawer: If we trace around the drawer you have perimeter, if you rub the bottom section inside the drawer you have area while if you fill your drawer with clothing you were measuring volume hence the inclusion of height (I guess more two dimensional for perimeter and area and three dimensional for volume). Thanks, Robert, for you example. Notify me of followup comments via e-mail. (Do you know how many adults can’t figure out cubic yards/feet to apply mulch!!) I just think that it’s a teacher’s job to make sure that everyone feels comfortable with a context. In Teaching Math With Story Problems, we talked about why math word problems are such a powerful teaching tool and why we should think of them as story problems instead. You could ask her to tell or show you what she knows. It seems like that is the case, yes. But I suspect that for many students for whom mathematics is just one big ball of confusion (cue THE TEMPTATIONS), their motivation is so low when they get to area and perimeter that they never make a point of processing the difference between the words, hence they don’t distinguish between the underlying concepts, and so “which formula should I use?” becomes guesswork.
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