Hi Sarah. Thank you so much. We are really excited about these learning trajectories, lessons, and the focus on UDL in the lessons. You can find the learning trajectories on our website: http://everydaycomputing.org/public/visualization/ We will be working on the website this summer, so come back later this summer as well as you'll see additional resources as well. 

Hi Susan. Thank you so much. We use various representations including: using both physical manipulatives of the math concepts (e.g., fraction circles) with the virtual manipulatives in our Action Fraction lessons (e.g., virtual fraction circles that the students manipulate). We also scaffold the projects in various ways. The TIPP & SEE strategy has the students go through a metacognitive strategy of thinking about the program before using and manipulating it. Lastly, for the open-ended lessons, we have multiple ways of allowing students to demonstrate their understanding through "base" projects and extensions to those. We provide project planning sheets to the students that have them plan their projects and get feedback, and we also then also have a simplified version for students who may not be performing at grade-level. I also have a document that I've been working on with several colleagues around UDL in CS education more broadly. You can find it here: https://docs.google.com/document/d/1gVKE_SSrvWd12NwhYMmg9k4u8dIfgr3TJRmHfos9XRs/edit 

This is a great question. We are unfortunately not collecting data on shifting student understanding as part of this project, although I would LOVE to do that. It's more an issue of capacity than desire. We are doing some think-aloud protocols having students explain their understanding, as part of validating our items, but this is definitely not getting at the complexity of the question you raise.  At this point, given the limited research in this area, we are only looking to see whether exposure to these integrated lessons improve students understanding of fractions (conceptual and procedural understanding) as well as CT understanding. Hopefully in another project!

Thanks Jeremy. It's incredibly challenging and exciting to think about access, engagement, and flexible learning within this context. We will have a long way to go, but this is definitely a good start! 

Hi, Beth! Thank you for your great question(s). I'm Carla Strickland and have been leading the Curriculum Development and PD work for this phase of the LTEC project.

To determine our approx. 12 hrs of instruction per grade level, we relied heavily on our curriculum development expertise and our knowledge of the CCSS for Math. Once we'd narrowed to the NF domain in grades 3 and 4, we decided an approximately once per week cadence during the Everyday Math fractions units would be manageable for teachers, which got us pretty close to that number. Our focus on the CT learning goals we wanted to cover from our Learning Trajectories (LTs) also affected the number, so once we picked the placement of our "anchor activities" we fleshed out from there —filling in activities on the other arrows of the LTs.

We do hope to eventually expand to other domains of both the math and CT content, but that is beyond the scope of the current grant. Fingers crossed for future successful proposals.

As for PD, we do 2–3 days in person, and provide online resources throughout the year of implementation. We carefully attend to both content and pedagogy by modeling instruction with our elementary teachers who are almost all completely new to the CS material. In fact, I'm currently prepping for lots of Summer PD, so if you or your colleagues are in the Chicagoland area, you are welcome to experience it firsthand! Please see our website for details: https://www.canonlab.org/ltec-2-pd

Fidelity is an important issue, but we tackle the brunt of this in our lesson design. The lesson layout and features are clear and familiar to teachers, so the modeling in PD just helps them hone in on how the new CS/CT content may adjust their classroom context and practice. We also encourage teachers to network with us and each other for implementation support throughout the year, which continues to positively impact fidelity.

Thanks again for your interest!

Thanks so much for responding. We are in Baltimore so it will be a long commute to Chicago but I would love to check in out in the future if you are closer to the Maryland area. Good luck with the study and i look forward to seeing the final results. 

Hi Mahtob,

It would be great to expand our work beyond fractions and grades 3/4 and hopefully, someday that will happen. We chose fractions as so many students struggle with them.  It seemed like an area of need, especially for students at grades 3 and 4 (CCSS) who were just beginning to run into some of the big ideas related to fractions, wherein misunderstandings can give way to misconceptions that impact student understanding for years to come. 

Thanks for your interest!

There's a lot of evidence that learning from worked examples can be very helpful -- something we all experience in our everyday lives when we learn "mimetically" by watching other people do things. Sort of the apprenticeship model.

On the other hand, there's also evidence that if every problem kids have to solve is immediately preceded by a worked example of a quite similar problem, then the kids are not all that likely to be able to solve problems in general very well. After all, one definition of a problem is something you don't know how to solve, so if kids only get problems they do know how to solve (since there's always a worked example), then they're not doing problem solving.

We think a lot about how to balance these approaches. When is it most helpful to give the kids a worked example, such as a working Scratch program, and when is it better to let them figure more out on their own? "Traditional" teaching approaches tend to over-emphasize telling kids stuff, but often when people try to correct shortcomings in traditional teaching they over-correct and are too undirected. Striking the right balance between learning by example and more open-ended approaches is tricky.

So, the comment in our video was a passing reference to a pretty big issue we wrestle with.

Hi Rebecca! I love your question! Thank you.

There are a few reasons we chose this movement, some more significant than others. On the CS side - this sliding motion is characteristic of the "move" block in Scratch. Students are very familiar with this block at this stage in the curriculum, so it was desirable to use it in this simple script they would be closely inspecting in order to debug the program. A hop motion (like a frog) would require more complex programming, but may have been worth it if we thought it was pedagogically appropriate for the math content.

Now on the Math side, which I think is the focus of your inquiry, we did debate whether the movement should be a hop or a slide. In earlier grades, students do hop along number lines for addition and subtraction. In these lessons, however, we are focusing on the NF domain of the CCSS. More specifically, this lesson references 3.NF.2, which requires kids to understand a fraction as a number on the number line. After talking with a couple other Everyday Mathematics authors, we decided the slide motion was more appropriate than the hop motion for this focus. In the next Action Fractions lesson we have the following text for teachers: "To reinforce the notion of a number line as a model for thinking about fractions, remind children that fractions on a number line are numbers representing distances from 0 to an endpoint." We use an EM problem in the Warm-Up, and ask teachers to "Move your finger along the number line to explain this solution to the class. For example, I started at 0. I moved 3-sixths and then 1-fourth to get to 6-eighths."

So in short, the sliding motion is more supportive of understanding a fraction as the distance from 0 to an endpoint in the number-line model. Personally, I also fancy the notion of kids potentially thinking about all the different numbers they may be passing on their way to the fractional endpoint. The frog is not hopping over these numbers, he is passing through them as he slides.

Please feel free to check out the full lessons on our website. Would love to discuss more if you'd like.

-- Carla