Learning Trajectories for Integrating K-5 Computer Science and Mathematics

Resource Release - Literature-based Learning Trajectories: Sequence, Repetition, Conditionals

August 16, 2017

The LTEC team is pleased to announce the release of our third public resource and first family of Learning Trajectories - the culmination of two years of work. These are being presented at ICER 2017 in Tacoma, WA in the paper K-8 Learning Trajectories Derived from Research Literature: Sequence, Repetition, Conditionals.

Our primary purpose in creating these learning trajectories is to help inform future curricular development by providing insight into possible content and orderings for major computer science / computational thinking topics. Learning trajectories have three components: An overarching learning goal, a partially ordered list of waypoints that suggest a path to the learning goal, and a set of activities that help students move along the path1.

Several steps were involved in creating these first three learning trajectories (more will be released as they are published). We began with a collection of articles now listed on our Resources page. For more information about navigating this collection, see our first Resource Release post. We extracted learning goals from literature and categorized them, as described more fully in our SIGCSE ‘17 paper, A Literature Review through the Lens of Computer Science Learning Goals Theorized and Explored in Research. We do not distinguish between waypoints and learning goals since they were all extracted from literature. Finally, we coalesced similar goals into consensus goals and created an ordering based on a combination of literature support and several heuristics described in our ICER ‘17 paper.

To see the learning trajectories, open the provided visualization tool. This tool provides a complete illustration of the Sequence, Repetition, and Conditionals trajectories. At the top of the page, there are several buttons with varying functionality. Clicking through these buttons will hide and show different subsets of information of the trajectories. For example, clicking the Beginning button will only show the nodes with “Beginner” difficulty, whereas clicking Advanced will reveal all nodes with difficulty up to and including “Advanced” difficulty. Clicking through each view button will reveal the Summary, Understanding, and Action goals of each node. Right clicking on a node provides a link to a list of the learning goals pertinent to the individual node. Right clicking on an arrow provides a link to the summary of an example activity, which would help students move from one node to another. Finally, we included a toolbar, with links to each of the different trajectories at the top right. We hope you find this tool useful. Please feel free to provide feedback in the comments about how we could improve it.

These initial versions of the Sequence, Repetition, and Conditionals learning trajectories were created using a specific method combining information from the literature and heuristics to determine orderings in the absence of guidance from literature. We are beginning a second phase in which we are seeking feedback from professionals in Computer Science education. If you would like to leave feedback on the content of the trajectories, please first read the ICER paper, explore with our tool, then fill out our LT Feedback Survey.


  1. Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical thinking and learning, 6(2), 81-89. 

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Resource Release - Computational Thinking and Mathematics Lessons

August 10, 2017

Since May of 2012, LTEC team members from the University of Illinois at Urbana Champaign (UIUC) and the Champaign Unit 4 School District have worked together to bring computational thinking into the classroom. Beginning in summer of 2013, Kenwood Elementary School embarked on a project to make computational thinking its magnet school identity. As part of that effort, they quickly realized that integration into existing content areas would be essential for implementing CS for all students. Beginning in 2014, Kenwood teachers worked together to develop lessons that would connect mathematics activities to computational thinking. Their mathematics curriculum was built around the Everyday Mathematics series developed at the University of Chicago.

The materials produced from this effort are now online. There are two units each for grades 1 and 2 and three units each for grades 3, 4, and 5. The materials are freely available on UIUC’s Creative Technology Research Laboratory site: http://ctrl.education.illinois.edu/ltec_materials

The activities are classroom ready in the sense that they contain connections to the standards, advance organizers for students, student materials and programs to edit, and teacher versions of the Scratch programs that are part of each lesson.

The process of development

Groups of elementary school teachers met on ten separate occasions to work on the lessons. They had support from UIUC faculty and staff, but the teachers themselves were the primary drivers for the content. They put their lessons in Google Docs that they shared among themselves; adding reflections after piloting the lessons and revising as needed. Two years later, as the LTEC grant was in swing, Judy Rocke, an experienced elementary school teacher, took on the role of general editor and formatted the materials in way to make them more broadly accessible. That is, she created a concise and uniform structure for the lessons.

Lesson features

The lesson components benefit from the pedagogical content knowledge of the instructors who created them. For example, the first grade lesson on animal stories does not assume much or any experience with Scratch. It provides the students with the blocks they need to complete the project. Planning pages are provided as advance organizers and pictures of sprites that teachers and students can cut out to make the project work more smoothly in a busy classroom. A checklist for assessment helps both the students and teacher know that the lesson is on track. On the other hand, the lessons are not so scripted that there is not plenty of room for further exploration. One of the joys of observing classrooms where these lessons are being used is seeing students engage in different ways with different understandings. For example, on one observation day, some students spent the period getting the sprites they wanted into position. Others finished this quickly and moved on to extensions like working on the background or programming tasks with code.org. When the students met on the rug together to share out at the end of the class, the teacher asked, “Do you have any ideas of what you would like to do with the project next?” “Make it move,” a child said, referring to the sprites.

As the lessons progress through the grades, the connections to mathematics become more obvious in terms of mathematical content. By grade four, students are animating the fractional parts of a collection of objects and creating a program that uses conditionals to prompt users for answers. The mathematics content is equivalent fractions, illustrating that 3/12 is the same as 1/4, for example.

We have used these materials to explore research questions around student collaboration and engagement. It is too early to say if mathematics learning is measurably improved by using these materials. What we can say is that the theme of Computational Thinking has been an important part of the magnet school’s identity, and creating and sharing materials has helped solidify that identity.

Try them out! Let us know what you think.

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Resource Release - Collection of CS Education Articles

August 02, 2017

The LTEC team is pleased to announce the release of our first public resource: a collection of CS education articles from scholarly and popular publications.

You can find the collection of articles on our Resources page. Articles are listed in alphabetical order by author. Click the “View Summary” link for any article to view a summary of the purpose, findings, and recommendations included in the article. When applicable, the summary page will also include information about the research methodology used in the article, including the sample size and characteristics.

Our primary purpose for creating this collection was to mine these articles for learning goals to use in the creation of our literature-based trajectories, which we plan to release in the coming weeks. However, we conducted our review in a manner that would also result in the creation of this resource for the CS education community. Additional articles will be added periodically.

We hope you find this collection useful. Please feel free to provide feedback in the comments about how we could improve it.

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LTEC Staff Profile: Andy Isaacs

July 20, 2017

Name: Andy Isaacs

LTEC Role: Principal Investigator

Professional Background: I am a Research Associate Professor at the University of Chicago, where I direct UChicago STEM Education, a center that’s devoted to research and practice in STEM education. I also lead the team responsible for Everyday Mathematics, the elementary program from the University of Chicago School Mathematics Project (UCSMP), and teach number theory for the University’s Urban Teacher Education Program.

I taught fourth and fifth grades in Chicago-area public schools from 1977 until 1985, when I joined the Departement of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago (UIC) as a lecturer in mathematics education. I came to UCSMP in 1995 to work on an NSF-funded teacher development project led by Shelia Sconiers. I earned a BA in classical Greek from Northwestern University in 1974, an MST in elementary education from the University of Chicago in 1977, and a DA in mathematics (with concentrations in abstract algebra and theoretical computer science) from UIC in 1994.

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