NSF Awards: 1742083

Integrating mathematics learning with computing holds potential for success. Computing builds upon many mathematical concepts and leverages mathematical thinking skills. Conversely, math achievement is linked with computational thinking skills. In particular, prior applications of programming languages such as R in math education have demonstrated a great degree of promise.

Yet significant barriers still prevent broad integration of these complex topics into math classrooms. Mathematics and computing are both highly complex and challenging domains on their own, and developing expertise in either is not easy. Combining the two successfully is more complex than simply providing joint resources. Instruction around such integration needs to juggle students’ cognitive load and sequence their learning. Any environment proposing to support integrated learning of these topics must leverage visual, dynamic representations to support mathematical conceptual development while providing extensive supports for novice programmers. We will develop code-editing, console-based control, coding history, interactive representations of mathematical outputs; scaffolding students during learning process; and integrating all of it together via a sequenced instructional approach that teachers can implement easily.

Computing with R for Mathematical Modeling (or CodeR4MATH) will provide a robust path for integrating math and computing learning. We will support students in integrated learning of the complex domains of math and computing, employing a coupled learning path that interweaves the two disciplines to generate mutual reinforcement. Leveraging R’s open-source ecosystem and STATS4STEM’s foundation, we will develop and deploy a learning platform integrating R computing resources, curriculum materials, automated assessment and tutoring, and teacher professional development resources.

## Kenia Wiedemann

Co-PresenterBenjamin Galluzzo

## Gillian Puttick

This is such interesting work, especially with the modern trend towards interdisciplinary workplace settings. I am interested to hear more about student outcomes using this approach. How are you measuring learning gains in math? In CS? Also how is the project defining computational thinking?

Benjamin Galluzzo

Kenia Wiedemann

## Kenia Wiedemann

Co-PresenterHi Gillian, thank you for checking on us!

Wooo! This will be a long answer. I will start with your last question! :)

We define computational thinking as the way one translates their ideas to computational models. The translation between the realm of ideas to a model occurs through computer code, built after brainstorming, generalizations, and simplifications.

The way we have been assessing how students’ computational thinking evolves is by proposing a step-by-step modeling activity and then switching to a more open-ended question, where we removed most of the scaffolding.

In one of our modules (shown in the video) we initially propose a situation where the student (or rather a group of students) play the role of a college advisor who is supposed to help other students to decide between buying a meal-plan or paying out of pocket for each meal. They are supposed to build a computer code that would allow them to help several students just by inputting their eating habits, lifestyle, etc. The whole classroom participates in the discussion, brainstorming and deciding what are the factors to consider, which ones are important and which ones can be ignored as a first approximation (student’s budget? Special diets? How often they eat? How much?).

During the activity, the CodeR4MATH platform offers support through instructions and R code snippets that students can modify as they wish and run to see partial analysis and results as graphs, tables, etc. They end up with a robust yet straightforward computer code that they can actually understand how it works. Wonderful! But this is just the first part.

Now… we propose a new problem, an open-ended question. This time we remove scaffolding, so they don’t have the code snippets, but they have a ‘template’ to serve as a basic code. Of course, the template code is too simple (by design). We want to see how they build the questions to improve the code and make it robust. What are the factors to consider and again, what is essential and what is not in a first approximation, how would you build on that first approximation to improve your model? The way they approach the problem changed. Students now start to see a big problem as made of smaller pieces. The activity we chose for this implementation is: we propose them to build a code that can become an app to help drivers to decide where to go to get gas when the gas light comes on. Students tackled the problem asking several questions. Where are the gas stations? What is the gas price there? Do I have enough gas to go? How do I know that? What is the car model? Am I driving in the city or highway? Do I have time? What is my ‘saving threshold’ to drive to another gas station? How much would I drive to save some bucks?

We collected their ideas and whatever piece of code they managed to put together. We got very cool responses such as “I don’t know exactly how to include this part in the code yet, but I would modify it to consider [this and that],” which is an important achievement in terms of computational thinking.

About 54% of students we interviewed said the activity kept or improved their interest in computer science. Even students who said that they didn’t want anything to do with computer sciences recognized that - at least - now they understand better the meaning of mathematical modeling. We are fine tuning our platform and activities based on our early results, and we are very excited about the next implementations!

Benjamin Galluzzo

## Kathryn Kozak

I teach statistics at a community college, and use R in my class. I am interested to see if this program takes off if students coming into my class will have some experience with R. Also, my grant, StatPREP, uses R to help students understand statistics better. The material for StatPREP has R written in the background using Little Apps, but users can see what the R commands are that are being used. It might be interesting if the two grants collaborated on what R commands and skills are being taught.

Benjamin Galluzzo

Kenia Wiedemann

## Jie Chao

Lead PresenterLearning Scientist

Hi Kathryn,

Thank you for your interest in the CodeR4MATH project.

I am also wondering what students would take with them into undergraduate study. As Kenia mentioned in her reply to Gillian, we asked students how the curriculum module influenced their interest in taking further computer science or programming related courses, and over half of them said the module made them more interested or reinforced their existing interest. I imagine these students would be more inclined to take R related statistics courses in college and be more comfortable with data-centric statistics and computer programming. I think it is great idea to investigate the actual impact on students’ behaviors when they enter colleges. We will explore the possibility of tracking and surveying the student participants in the following years.

I like StatPREP materials a lot! I believe K-12 math teachers would benefit from using these materials. Many high schools that we have been working with are moving statistics to early years and placing it into required courses, as recommended by the Common Core State Standards. It would be great to provide students the opportunities to use R to statistics when they are in 9

^{th}or 10^{th}grades!Jie

Kenia Wiedemann

Benjamin Galluzzo

Kathryn Kozak

## R. Bruce Mattingly

This is a very compelling project. As you track students' interest in taking more computer science/programming courses when they enter college, are you perhaps looking more broadly to see if they also look for opportunities to take courses in mathematical modeling, data analysis, etc?

Benjamin Galluzzo

Kenia Wiedemann

## Kenia Wiedemann

Co-PresenterHi Bruce, that's a great question, thank you!

We collected data on how students perceived their understanding of the meaning of mathematical modeling after the activity and whether it has changed from what they understood as math modeling before. Eighty-three percent of the participant students (yay!) indicated that the activity helped them understand the concept of math modeling better (or much better). That being said, it would not mean that these students would be interested in pursuing courses related to math modeling, data analysis, etc.

More broadly (finally getting to your question) we asked the same students to describe their careers of interest at the moment. Fifty percent of them said they were interested in careers in STEM, Computer Science, Math, and Social Sciences (such as economy, so very much likely to make use of a lot of data analysis, modeling, etc). On the other hand, 31% of students were interested in careers related to the Humanities (arts, law, journalism, and such). Sixty-five percent of these (i.e., ~20% of the total) don't want to have anything to do with math sciences.

It is my interpretation that although the activity has helped them understand what math modeling (and data analysis for that matter) is and how it works in real life, they feel it's just not their cup of tea. And that is okay.

It will be a great idea to expand our pre/post-implementation questionnaires to include questions that target interests other than computer science and programming! Thanks very much! \o/

Kenia

Benjamin Galluzzo

## Matt Fisher

This is a very interesting project that I see having lots of potential interdisciplinary connections throughout STEM! The first round of questions that I had after watching the video (yes, definitely more than one question) were:

1) Towards the end of the video, one of the speakers mentioned hoped for improvements in critical thinking. I would be interested to learn more about how you hope to gather evidence of any changes in this area.

2) Has the project reached the stage where you are starting to talk to STEM teachers outside of math? As a biochemist, I immediately saw connections between your project and some of the ideas in systems biology. With some of the recent calls to strengthen the background that undergraduate biology majors have in computational thinking, the project could be a really good resource for that.

3) Have you thought about the potential impact of this project on student understanding of mathematical modeling in the context of civic issues like climate change (particularly efforts to predict future changes in climate and impacts of climate change) or public health (modeling the spread of diseases)?

Benjamin Galluzzo

Kenia Wiedemann

## Kenia Wiedemann

Co-PresenterHi Matt,

thank you for your questions! I will try to answer them in a different order. :)

(3) Yes. We went through some exploratory analysis with some students to see how they would perceive climate change through the lenses of mathematical modeling and data analysis (specifically with R in this case, but not necessarily). We explored real NOAA extreme weather data (in the US) and the students that 'signed up' for the activity were very receptive. I am a physicist and an environmental scientist so the subject speaks to my heart. ;) What I could observe is that motivation is the key. Seems a commonplace affirmation, but, see, people hear the term climate change too often (for a reason!) to the point that we are risking to make people numb to the problem. Does it make sense? When students started checking real data and could relate what they were seeing in graphs and such to events that actually happened, the problem becomes palpable again. They google, learn about what happened to the population affected by an extreme weather event, for example. It creates empathy (hopefully), which increases their motivation, and so on. Regarding public health, that is on the plate as well. We have some materials already in preparation, although we are not touching subjects like the spread of diseases. We have real data for analysis connecting mortality rates and economic development, etc. I, personally, have a great interest in exploring math modeling for population analysis (spreading of diseases lies well under this umbrella).

(2) That being said, the project is mainly focused on math classes, therefore we have been working with math and computer science teachers only. Although we haven't reached STEM teachers (yet?), there is inherent interdisciplinarity in this project. While we are already tackling subjects like personal finances, other subjects related to earth sciences, and engineering (e.g., solar energy) are in the waiting list for the next implementations. Exploring accessible subjects (to high school students) in systems biology is a great idea! The message we would like students to get home is that mathematical modeling is everywhere. Learning that through a subject of their interest seems to be the key! As a biochemist, would you have some recommendations on where to start? That's okay if it is based on your preferences; it's a healthy bias. :)

(1) (Finally!) We hope to gather evidence of any changes in students' critical thinking letting them study open-ended questions AFTER being guided step-by-step to work on math modeling to solve a problem. We remove the scaffolding and let them “go wild” in building not only an answer to a question, but asking the questions themselves, and then finding solutions to those questions. We compare how their questioning about a problem changed in nature. We still have limited data, but we see that students who seemed stuck before the initial activity, now become more upcoming, asking thoughtful questions, guessing outcomes, questioning assumptions, and so on. They seem to become more open-minded because no question or assumption is 'stupid' in principle. Does it make sense?

Benjamin Galluzzo

J. Owen Limbach

## Matt Fisher

Hi Kenia,

Thanks for the long and thoughtful reply! What you wrote makes a lot of sense to me.

As far as possible systems biology topics to approach from the perspective of mathematical modeling, perhaps something related to metabolism and homeostasis might be a good place to start. That subject would have the advantage of being easily connected to issues like diabetes.

Benjamin Galluzzo

Kenia Wiedemann

## Kenia Wiedemann

Co-PresenterHa! My middle name should be "Prolix."

That's a great suggestion, Matt. Hmm... Students could start the conversation by the big picture (diabetes, for example) and then work on 'smaller' parts of it, like the modeling process in homeostasis, tolerance limits, feedback, etc. Not being a biologist (or a chemist), I hope I didn't say anything insulting to biochemists! :)

Benjamin Galluzzo

## Peg Cagle

CodeR4Math seems to build a gentle on-ramp for high school students to become both proficient and curious about CS in general and coding in particular. I am especially intrigued about the description of the way in which students are enticed to dig further and explore more, by building small capacities, then giving them opportunity to see what those capacities can answer, but also new questions that get posed in the process. This design evidences a nuanced understanding of adolescents, their learning, and the all too frequent phobias student harbor about plunging into the deep end of math. AS mathematical modeling becomes infused into more math courses, I am curious if you see this having a role in lower grades such as beginning high school or even middle school, and what modifications might be needed to make that successful?

Kenia Wiedemann

Benjamin Galluzzo

## Benjamin Galluzzo

Co-PresenterHi Peg,

In response to your question about modeling in lower grades; yes, I definitely believe this approach can work. Many of the problems we are presenting to students are able to be investigated using mathematical skills many students encounter at the grade levels you identified (and in many cases, even younger!). The math isn't the roadblock, rather, it's a lack of experience with math modeling and coding. One thing we're learning is that we need to provide even more scaffolding for some of our students. With a more extensive "network" of scaffolds (and for teachers, scaffolding tools) in addition to providing more levels of access for upper level high school students we'll also be able to reach students (and teachers) at lower levels and have resources that allow for teachers to infuse into their curriculum at a classroom-specific (and eventually student-specific) pace.

Kenia Wiedemann

J. Owen Limbach

## Euisuk Sung

This is a truly great project. I believe students' early exposure to engineering or computer science is always good. However, as you noted in the program description, I also agree that still there exist some barriers such as learning curve for learning CS concepts, students' low interest, prerequisite knowledge to learn the complex CS and math concepts. I am wondering if you have had any challenges due to the students' failure in programming. I am a big fan of R but my colleagues are hesitating to use R because of coding.

Kenia Wiedemann

Benjamin Galluzzo

## Benjamin Galluzzo

Co-PresenterHi Euisuk,

Thanks for the comment and question. A significant focus of our project is to motivate the need for coding by connecting "new" (to many students) programming ideas (e.g., snippets of code for plotting data) as part of the scaffolding for real world problem solving through math modeling. We are finding that some students "get it" but that there is some need for additional (finer) scaffolding so that all students can (at first) comfortably navigate through a project.

Kenia Wiedemann

## J. Owen Limbach

I loved hearing the perspective of the teacher in this video who talked about being able to effectively lead classes in coding with very little personal background in the subject. Computer technology has been moving so quickly that there is an extreme supply-and-demand problem country-wide. There are just not enough teachers with high levels of coding skill to train the next generation. Knowing that there are ways to get around this issue and allow teachers to expand into these new types of classes even when they have no background on the subject seems really promising. Thank you for doing this work!

Kenia Wiedemann

Benjamin Galluzzo

## Edith Graf

This is great work! It sounds like you are using R very effectively to support students' mathematical modeling and data analysis practices. It seems to me that learning to code in R might also enhance students' mathematical conceptions of variables and functions. I was wondering if this is something you plan to assess?

Kenia Wiedemann

## Kenia Wiedemann

Co-PresenterHi Edith, thank you for your interest in our project.

The short answer is 'yes,' is part of our goals to make these concepts more tangible to students. The concept of variables is sometimes difficult to grasp, it depends on the context and the media students are using. When students are coding, we try to introduce 'variable' as something that MAY vary, instead of something that varies for sure. In that sense, they start to understand that what one call variable may mean a constant in a specific context/code.

The concept of function may cause some confusion in the beginning, but we have been able to address the difference between the mathematical function (which they are mostly used to) and the programming language functions, which at the end of the day are actual codes written to perform a task. For the next implementations, we are planning some short activity to make both concepts crystal clear to students. :)

Edith Graf

Further posting is closed as the showcase has ended.