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LTEC: Learning Trajectories for Integrating K-5 Computer Science and Mathematics

The University of Chicago’s Center for Elementary Mathematics and Science Education and the University of Illinois at Urbana-Champaign’s College of Education propose a two-year STEM+C Track 1 Exploratory Integration project, "EI: Learning Trajectories for Integrating K-5 Computer Science and Mathematics," which will create prototype learning trajectories for computer science at Grades K-5. Each trajectory will span multiple grades and will include a target goal, intermediate objectives, performance expectations, sample tasks and assessments, and hypothetical learning paths. The prototype learning trajectories, including the sample tasks and assessments, will be designed to fit with Everyday Mathematics 4 (EM4), the elementary curriculum from the University of Chicago School Mathematics Project.Since EM4 is newly revised to closely align with the Common Core State Standards for Mathematics (CCSS-M), the tasks and assessments will also be usable with other instructional materials aligned with CCSS-M. The learning trajectories (LTs) will be developed and tested in collaboration with 18 teachers and 4 teacher-leaders in public schools in Champaign, Illinois.

## Katie Rich

PresenterHello, everyone. Thank you for visiting our video! I'm Katie Rich, one of the co-PIs of the LTEC project. We're interested in hearing your feedback and answering your questions about the project. In particular, we've been discussing these questions, and would welcome further thoughts:

How do we make our trajectories flexible enough to support the open-ended, constructionist style tasks and projects that characterize much of current CS instruction?

What information would various audiences (e.g., researchers, developers, teachers) want to see when examining our trajectories? What would a helpful, easy-to-use presentation of the trajectories look like?

Where within mathematics instruction do CT concepts best integrate? How can we best help teachers and kids to see the connections between the subjects?

## Meg Bates

To me, the trajectories will be salient to teachers if there are clear examples of what students who have mastered the knowledge in something like the "conditionals trajectory" look like. This is, I suppose, an assessment question--if a student knows something in the trajectory, what are they able to do to show that they know it? Have you given any thought to how the information in the trajectories will be actionable for teachers in this way?

Katie Rich

## Diana Franklin

Co-PresenterIn our more full depiction of learning trajectories, they are specified in two parts - learning goal and activity. This activity could be used either as a teaching tool or an assessment tool, depending on how the teacher leads the activity. We are also considering hanging activities onto arrows to explicitly be teaching activities in order to move students in their understanding.

## Katie Rich

PresenterHi Meg,

Thanks for the comment! In the full versions of the trajectories, which we hope to make publicly available on our website soon, each "box" on the trajectory has two parts: an understanding goal, which attempts to articulate the broad understanding we want kids to have, and an action goal, which attempts to describe something the kids can do to illustrate that understanding.

We think the actions will be helpful to teachers, but have wondered if such specific articulation of them will lead the trajectories to be used for tracking kids into ability groups -- something that we don't want. We hope to eventually allow public contributions to the trajectories that allow teachers and others to comment and add their own ideas of how to track understanding. We'd welcome any thoughts you have on the pros and cons of this.

## Meg Bates

Ah, thanks! That makes sense.

I understand your worries about ability grouping, but that is the danger of providing any kind of assessment data. You have to take the good with the bad on that, I fear.

I do think asking teachers to add exemplars would be a cool idea. That would make it feel less assessment-like and more illustrative. Your issue will be motivating them to do so!

You mention towards the end of the video that you still need to fully merge goals found in practice with goals found in the literature. Another issue I'm curious about is if/when you will merge math goals with CS goals and whether you are doing that primarily to motivate teaching of CS by situating it within a core subject (which is a fine aim), or whether you have observed that CS and math learning are improved by the integration? If the latter, what evidence have you seen of students' improved understanding of shared concepts in math/CS (and for what concepts)?

If you haven't gone there yet, I understand! There's only so much work you can do. :)

## Katie Rich

PresenterGood question. We're working now to attach illustrative activities to the trajectories. We're going to try to use math-situated activities as much as possible. That will be our route to merging with math -- not so much a direct mapping of CS goals onto math goals, but rather creation of activities that have both math and CS learning goals. We suspect that sometimes the goals will be shared. For example, both math and CS have embedded conditional thinking. But often the goals may simply be complimentary. For example, drawing polygons has in the past been shown to be a good fit for thinking about computational loops.

As to the motivation for this, I think there are aspects of both of the reasons you propose. We want to situate CS in a core subject to help make sure all kids get the instruction, and to leverage existing math knowledge in teachers and kids. But we also know that past integration of math and CS have been successful, with decades of work with Logo being a prime example of that. We don't have well-founded evidence of positive learning effects from our own work just yet, but we do have plenty of anecdotal evidence from our pilot teachers that kids have responded well to CS/CT + math instruction.

## Maya Israel

Co-PresenterHi Meg. I appreciate your question about merging the trajectories for the math and CS/CT. Thus far, at least from the practice-based progressions that we are developing from classroom implementation, we have found this to be challenging. Our first level of analysis are the lesson plans. These have clear math learning progressions, but nebulous CS/CT progressions. As we are constructing the CS/CT progressions, we are still testing out what we think students are learning at different grades. I believe that once we have more flushed out learning progressions in CS/CT, we might be able to look at integrated progressions. In the meantime, we are having conversations about the intersections of the progressions, but this has not yet become a formalized approach.

## Ben Sayler

I'm curious what's tricky (for children and adults alike) about conditional thinking. I get the idea that computers need to be told what to do when a condition is not met, whereas humans tend to infer this. That's interesting - and a new idea to me - but it doesn't seem especially tricky. I'd love to hear more about this.

Diana Franklin

## Katie Rich

PresenterHi Ben,

Great question! From what we've been able to gather, it seems the tricky part has to do with the precision in instructions required in programming. It's not intuitive for people to explicitly state what do to when a condition isn't met. So, when that instruction is left out of a program, it's not particularly intuitive to realize that is the problem when debugging. Generally, it seems that it's easier to check the code already on the page than to think about what might be missing. This notion of specifying the action connected to the false state is a context where that situation might come up -- not incorrect lines of code, but missing lines of code.

Interestingly, I had never really thought about the intersection between this idea and debugging before, but your question helped me articulate it. Thanks! This might be something we investigate further in our next round of work.

## Diana Franklin

Co-PresenterI also think the degree of difficulty matters.

In Scratch, for example, there are a lot of events. It is pretty easy for fairly young children to think about what they want to happen for each event. This is a form of conditional thinking, and it appears to be pretty easy for little kids. However, this is a simple If user does this, then do this. There is no notion of what to do if the user *doesn't* do that action, as Katie alluded to.

It's a lot more difficult either there are more than two choices (requiring the students to specify the choices using nested statements or complex logical expressions), the conditional is partway through the code (I'm doing a bunch of things and then, at this point, I only want to do X if this is true and Y if not), or if the amount of stuff to do in the conditional is a lot. All of this puts more cognitive load - more things to keep track of - than just specifying 10 steps in order to accomplish.

Dr. Lisa Milenkovic

## George Reese

Co-PresenterHi Ben,

When I watch kids at the school we're working with, they have tasks that the teachers have structured for them. The tasks require events to take place on cues. For example, they want to switch a background after a sound has played. A problem they run into is needing to use the "Play until done" block.This somewhat primes them for the next effort, which is to envision a user of the code and request an interaction, "What is...." they ask the user, and then they have to handle the response. It seems natural to me that this problem occurs, but, as Katie says, no necessarily intuitive what to do if the condition isn't met (for children, not getting the response they expect). This debugging seems the hardest part. Though, I have to say I am impressed with the patience the kids I observe seem to have with trying to figure things out. Many times, I see a child with one hand in the air hoping to get a quick answer from a teacher, and the other on the mouse trying things at the same time.

## Jennie Lyons

The lack of learning progressions in CS makes this challenging. Is there a parallel outcome for the "condition not met" concept in math and computer science? I'm looking forward to the results re learning goals for both CT and CS and very interested to see if the outcomes are the same.

## Katie Rich

PresenterJennie,

Definitely! We're trying to fill a big gap by developing our LTs and structuring our future research around strengthening them.

I don't think there's a perfect match for "condition not met," but one place in mathematics where the same issue comes up is in generalization of methods and case-based proofs. I think of the broader idea as thoroughness in reasoning. While I can't claim to have figured out how to go about this, it seems to me that leveraging places where a need to "cover your bases" comes up in each discipline is a place to start.

## Diana Franklin

Co-PresenterBouncing off Katie, if "condition not met" has a place in mathematics in thoroughness and "covering your bases" with proofs, then a location in CS with synergy is testing methodology. We would want a set of test cases and expected results. This also feeds into our debugging LT, which we are currently developing.

We have actually been able to find math/CT synergies with most concepts by scouring the Everyday Mathematics curriculum for examples. There are a lot of mathematical games they play in that curriculum that include conditional decisions. Moving it to CT requires students to specify the rules they were already using that they might not have identified precisely.

## Ben Sayler

Very cool. I've learned a lot from this "condition not met" thread. Thank you!

## Jennie Lyons

I am so excited to see this. CS K - 8 curriculum is really beginning to take off, and having more defined LTs and integration will certainly pay off in the long run. (Not to mention the short-term.)

Dr. Lisa Milenkovic

## Kip Glazer

I love that you are working to bring together "the prior research and current practice." I am just curious as to how you work with the teachers who have additional requirements such as grading and tests. I would think that you would have to use terms or concepts that would speak to the teachers. I ask because we are coming to the end of the semester at my school, and the deadline to submit grades are on my mind.

## George Reese

Co-PresenterHi Kip,

We are working with two groups of elementary teachers. One is a diverse public school that has adopted computational thinking as a theme. So they have a technology coach that helps and some of the teachers have worked with us to create lessons.

Other teachers are trying modules in schools that don't have those supports. However, we've tried to create activities that fit within the Everyday Mathematics curriculum, so that they reinforce and expand upon the math activities they are already doing.

Fitting it into the school day is one of the reasons for trying to do the integration. Teachers' days are already full, and it's difficult to add coding and computational thinking as a whole new area. The great thing is that kids are so into it that it's not a hard sell, and this makes teachers want to learn more.

Further posting is closed as the showcase has ended.