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## Topic: "What does integration look like?"

### Topic Posts

### Topic started by: Katie Rich on 2/29/16

I'm interested to hear what others think about what successful integration of CS with another topic looks like. For the sake of discussion, I've been doing a thought experiment about different activities that integrate fraction addition and conditional statements might look like. (I'm not arguing that these two topics are good or bad to integrate; I only mean them as examples to allow me to think more concretely.)

1. Students have previously learned how to add fractions, and now they are writing programs about word problems that other students can solve. They want to give feedback on the answers that other students enter, so the idea of conditionals is introduced as a way to tell the computer to display different feedback according to whether the answer is correct or incorrect.

2. Students have previously written programs with conditionals that determine feedback, similar to what I described in (1). Now the teacher poses a problem involving fraction addition and asks students to write a program about that problem. Students realize, when they go to designate the correct answer, that they don't know how to calculate it. This motivates an unplugged activity to learn how to add fractions. Students return and complete the programs after some practice with fraction addition.

3. Students have worked with both conditionals and fraction addition before. As they write their programs, rather than directly entering the correct answer to be matched with student input, they are asked to write the program to calculate the answer automatically. That is, they have to generalize the method they learned for fraction addition so the computer can use it.

Are all of these examples of integration, appropriate at different times? Are some better for different ages than others? What are the benefits and costs of each? What are some other examples of integrated activities?

### What I've seen so far

posted by: George Reese on 3/1/2016 7:15 am

In the elementary school classes that I've been observing teachers have gone out of their way to incorporate the conditionals in the context of fractions. Honestly, it looks like a force fit in many ways, because it is. I believe this is a function of teachers having such limited time. The math content to be "covered" is a given and then the programming activity is put on top to animate the fraction story.

Despite these constraints, kids do some creative work exploring the network to add sounds and put some bells and whistles in their programs that make the work their own.

But it still feels like we're in early days as far as integration goes. Trying out activities within time constraints and as add-ons rather than real integration. But it does seem to me that elementary math is the right place to start. It gives students and opportunity to put some creativity around a fraction concept, even if it's just a "here is my portion" idea.

-George

### Where to go from here

posted by: Katie Rich on 3/2/2016 10:29 am

Thanks for the response. I agree with you that we haven't reached the point of true integration. In general terms, I'd characterize the three examples I gave as:

1. Using a math topic as a context for introducing or extending CS ideas. Students practice some math while doing CS, but don't really learn new math through the activity. Most integrated activities I've seen so far are variations of this approach. I think there is a place for such activities -- as you say, a place for kids to express creativity is never a bad thing -- but I think we can do better.

2. Using CS as a motivator to learn new math. Kids realize the need for further math learning via a CS activity, but still don't really address both math and CS at the same time. This feels rather forced to me, particularly since computers can easily do the computation kids are learning to do.

3. Making mathematical generalizations in service of writing a computer program. This, I think, is the example that's closest to an activity that uses similar practices to integrate two areas of content. It sounds good to me in theory, as it gives a clear context in which a generalized mathematical algorithm can be useful. However, I don't claim know how to execute such an activity in a way appropriate for elementary school kids.

I agree that elementary math feels like a place ripe with possibilities for integration. I'm just trying to define for myself what successful integration looks like, and I'm interested if anyone has tried models different than the ones I described.

### Re: Where to go from here

posted by: Andrew Isaacs on 3/3/2016 7:42 am

Very interesting thread you've opened. Thanks much.

I recently read an article by Seymour Papert (http://www.papert.org/articles/AnExplorationintheSpaceofMathematicsEdu cations.html) in which he gives an example that seems not to fit so well into your three categories, which I think you're not claiming are comprehensive but are simply characterizations of your several examples. Papert describes several solutions to a problem in plane geometry in part 5 of the article, "Rugby Session," including a couple based on classic Euclidean geometry, either pure paper-and-pencil or powered by Cabri, and one that he cooked up using the random function in logo. He argued, and I agree, that his method involved a fundamentally different approach, one that involved computation to generate mathematical insights not so easily available via a more traditional approach. I think his solution is a nice illustration of math + computational thinking, though at a level quite a bit higher than elementary.

### Re:Where to go from here

posted by: Howard Dooley on 3/4/2016 9:02 am

### Direct link to article

posted by: Katie Rich on 3/4/2016 3:21 pm

### 4th integration type

posted by: Katie Rich on 3/7/2016 11:50 am

You are correct that my categories were not meant to be comprehensive, but rather just a starting point for generating a much longer list. I agree that Papert's example is a fourth category, which I would characterize in general terms as (borrowing some of your words):

4. Using a CT strategy to solve a mathematical problem in order to gain a different viewpoint on the problem. This is different than using computing because it is more efficient or generalizable as hinted at in my integration type 3.

What other types have others seen?

### Re: Where to go from here

posted by: Emmanuel Schanzer on 3/8/2016 7:11 am

This seems like the holy grail of integration to me - any other approach (teach A in service of B, B in service of A, use A to motivate B, etc). Grails are hard to find, so perhaps that's why it didn't make the cut for the top 3? :)

### grail, indeed

posted by: Katie Rich on 3/30/2016 10:12 am

This is the big challenge, I think. There are plenty of shared concepts, but the application of the concepts is different in math versus CS -- that is what makes them different disciplines. So when it comes to what kids *do*, rather than the broad concepts they're addressing, I have a hard time conceptualizing an activity that puts the two disciplines on equal footing.

Anyone have an example of the "A and B" approach? Even a pie-in-the-sky idea?

### computational thinking in K-8

posted by: Amy Cohen on 3/2/2016 10:44 am

Amy

### re: computational thinking in K-8

posted by: Emmanuel Schanzer on 3/3/2016 7:33 am

The evidence of transfer from programming into algebra is pretty hard to come by, but it's a tough problem we've been on for many years at Bootstrap. We've been able to repeatedly demonstrate significant impact on regular, pencil-and-paper algebra tasks, and we've published our outcomes at http://www.bootstrapworld.org/impact/

It turns out that programming CAN help teach algebra, but it takes far more than bells and whistles: it takes mathematical alignment at the pedagogical, curricular, software and even programming language level.

### Why integrate?

posted by: Katie Rich on 3/7/2016 11:57 am

These are good questions, and I think we know some preliminary answers but as Emmanuel points out, there isn't a lot of evidence of transfer.

Your post generates a number of related questions for me, all centered around the big question of why we want to integrate in the first place:

1. Do we think there is potential for integration to enhance learning in one or both of CT and the subject in which it is integrated, and we just have not quite figured out the best approach?

2. Are the other arguments we discuss for integration (e.g., no room for a brand new subject in the school day) compelling enough to make integration worthwhile even if it does not enhance learning or transfer? Is making room where there is no room enough, even if we only maintain the status quo in other STEM learning?