Problem Solving Series: The Early Years

Oct 20, 2017

In the Kindergarten or 1st grade classroom, especially within the Math Workshop, it’s almost impossible to have a Math with Writing station where kids are actually reading and solving story problems without needing any kind of help to decode what the problem is asking and know apply how to apply addition and subtraction processes to that concept. We typically say that Math with Writing should be up and running around 2nd grade, so what does problem solving actually look like in Kindergarten and 1st grade?

the early years

In Kindergarten especially, it’s a whole oral language experience. Once they understand numbers and counting (for example, 7 can be decomposed into 5 and 2, or 3 and 4), they start to understand that they can play with numbers and actually be able to write digits. For problem solving, we want to help students to be able recognize that numbers can be applied to real life situations, which is mostly where they will encounter numbers in their future world.

A big part of where we start problem solving in Kindergarten is through the use of real pictures and related stories. The application of math practice #2 (I like to explain it as “numbers to words and words to numbers”) is really thinking abstractly and quantitatively about math. Students quantitatively understand numbers, but we need to put them into a real life situation to help kids recognize what those words are actually doing.

Just like we aim to get our number talks in 3-5 days per week, we have to make time for problem solving. That is where the similarities end, however. Math and number talks are very different in the way they are delivered in a classroom. Simply put, a math talk is getting a conversation going where students are translating numbers to words and words to numbers. This will only take 7-10 minutes in a Kindergarten classroom. One of my favorite resources for problem solving is Math Talk: Teaching Concepts & Skills Through Illustrations & Stories, by Char Forsten and Torri Richards. In a math talk, teachers display a real picture that is from the book or similar quantitative picture, like the hidden pictures in “Highlights,” where there are multiple things going on in the picture that could be related to quantities.

Math Talk is a great resource for questions – they provide beginning questions (1 to 1 counting), intermediate questions, and of course, advanced questions (“If there were five spiders and one of them walked away, how many are left?”). The different levels of questions help you bring in addition and subtraction concepts, or higher level concepts (ex. “How many legs does a spider have? How many legs would two spiders have?”). This is a big portion of what happens in problem solving, but we want to take it a step further before children move into their first grade year.

There is a free download with lots of great pictures from the Math Talk book that you can use with your class. You can get the download for free, however, we still highly encourage you to buy the Math Talk book because the book will provide the questions you can ask as you have conversations around each picture. You can also take advantage of the digital copy of the colored images to display on your interactive whiteboard, enabling students to touch and interact with the image. The book also comes with black and white coloring pages that you could use to do some great things with kids at the carpet area, such as “Color in the triangles. How many triangles do you see?” Download the PDF here: http://www.sde.com/mathtalk.pdf

Once the teacher displays a picture, the students would look at the picture and start interacting, eventually being able to ask questions about what they see. You might start out asking them concrete questions such as how many spiders do you see? Or you might say, I see bunnies hopping over the fence. How many bunnies do we see all together?  Then we want to make the questions a little more complex, for example: I see bunnies. I wonder how many legs the first two bunnies have? Or I see four bunnies, and I wonder how many eyes they have all together. The objective for this type of questioning is to help kids engage in conversations about real life pictures so they see that stories can be put together with numbers.

journal template roadThe other aspect to problem solving in Kindergarten is to get kids to start to act out these different topics. Math talks do involve a lot of conversations, but we do want students to be able to hear a problem, act it out with manipulatives, eventually be able to make a quick drawing and (if possible) a number sentence. One of the ways we do it is to use the Math Work Mat area of our PreK-K Math Journal Templates that I created. Each has a different setting in the background and they were intended to be very open-ended.

The possibilities for using these templates are endless! In one example, you could have the students sitting with their Math Work Mats in a circle at your carpet area and have a pile of unifix cubes in the middle. You could have the Road Journal Template out, and tell the students you want them to be able to show you one car on the road, and then a motorcycle on the road. You might talk about the number of wheels the motorcycle has or the number of wheels a car might have. We’re hoping that the students will put four unifix cubes on the mat to represent the car, and two cubes to represent the motorcycle so they can see that there are six total wheels on the road.

You want to make sure that you make your questions and scenarios a little more complex as the year goes on. “There are two piggies in the corral, and three more join them. How many are there all together?” This a good starting point, but it is a pretty “thin” question and over the course of the year, they should become more complex.

An important thing to remember with Kindergartners is many of them are skipping their imagination stage because they’re plugged in to something electronic so often. The imaginative play element is also being taken out of Kindergarten, and kids have a really hard time imagining that the counter or a unifix cube as an actual inanimate object. So, if I say wheels and am actually using unifix cubes, I will likely have a few confused students pointing at them and saying “those aren’t wheels – those are cubes!” Kids need a lot of help using manipulatives on the mat and having someone help them act out the problem.

journal template treeUsing a different template (the tree), you might ask something like this: “I see three owls in the tree, how many eyes (or wings or anything else) are there?” You can use the top portion of the Math Work Mat at the beginning instead of having them do the quick draw every time. As kids get better with this, you can slowly start to integrate the journal templates to get the kids to do a quick draw.  This is a challenge in Kinder because you’re still trying to teach them that people don’t really have blue hair and to make their pictures more detailed and accurate. In math, however, we don’t want our drawings to contain a lot of details, we just need quick information.

Let’s say they were drawing owls in the tree in a quick draw on journal template mat. (You don’t have to be an artist, FYI!) You might have the kids draw a circle with two dots, maybe add a little beak nose, to represent the picture. Over time, and especially before they go into first grade, they need to be able to do a quick draw.  For example, if I was drawing the cars, I would draw a circle with four dots, or four ‘x’s, to represent the car. Then, I might have another circle that has two circles or ‘x’s to represent the motorcycle.

If kids are able, we would then like to see them label their drawings. If they were counting the wheels above (the four dots), they would write that one was four and one was two for a total of six wheels all together. So, 4+2=6.

buildingThis is the whole development of story problems in order to really help prepare kids for what they need to do when they get into first grade. The idea of laying foundational problem solving skills in the early years is to build oral language, to build children who are able to act out real life situations with concrete objects, to be able to do a quick draw, and then, hopefully over time, to be able to write a number sentence. This will help prepare them in the long run as we start to get into first grade, because in 1st grade, we’re going to do a lot of part/whole problems and comparison bars.  We really want kids to start to do actual story problems in 1st grade, but it would be very appropriate to use this model in a first grade classroom within the first month or two of the school year to help kids remember “numbers to words and words to numbers” before they move into more complex story problems that they will encounter in the rest of 1st grade.

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