NSF Awards: 1759195
2021 (see original presentation & discussion)
Grades 6-8, Grades 9-12, Undergraduate
This video describes a research project that examines how practitioners in STEM and STEM-related careers use algebra to do their jobs, and then uses this information to build classroom activities for students enrolled in algebra courses. Students posed, solved, and shared algebra problems relating to their career interests in an online environment housed in the ASSISTments platform. Students learned how algebra was relevant to their careers through video clips of current practitioners describing their use of algebra, example problems about how algebra is used in their career, and templates where they could build their own algebra problem relating to their career. We show how 8th graders, high school students, and community college students all used this environment to learn more about their careers and gain a deeper appreciation of algebra.
Candace Walkington
Associate Professor
With funding from an NSF ITEST grant, our research team has for the past 3 years been investigating how algebra can be connected to careers students are interested in. We'd love to engage with you!
Feel free to ask us any questions, or discuss one of these topics: (1) Who should learn algebra? What should be included (or not) in algebra courses? What is algebra really useful for? (2) What are some powerful applications of algebra that you know of? (3) How can making connections between algebra and the math used in different careers be done effectively in middle school? High school? College?
Ateng' Ogwel
Ateng' Ogwel
Candace,
Thanks for sharing the ideas in your project. It's critical for students to see the bigger picture of how mathematics is applied in careers to justify that why mathematical literacy is important for all. We have situations where even those who use mathematics may not be aware or are hesitant to admit that they are using mathematics.
Your team's choice of algebra is strategic, given the documented challenges in learning if algebra. Ill be keen to learn from your project if there are reports on how the strategies could be deployed to a slightly expanded scope
Michael Belcher
This is such a cool idea! I love the range of choices students have in identifying a career interest! We've been working on a somewhat similar project, where we've been trying, in part, to introduce career connections in middle school math through entrepreneurship. One of the difficulties we've had is helping students to realize that what they are doing counts as math. In my dissertation study, for example, even though students wrote and manipulated symbolic expressions while building spreadsheet algorithms, they tended to only consider instances in which they calculated sums or products by hand as doing math. Your project seems like it addresses this challenge really nicely by explicitly highlighting connections between the career and familiar (to students) math. At the same time, how do you allow for and demonstrate the creativity that is possible in these careers and avoid making the careers seem procedural? How are students responding to it so far?
Anyway, great work!
Kimberly Elliott
Matthew Bernacki
Candace Walkington
Associate Professor
These are great questions! We try to deal with this problem through lots of scaffolding. We show students examples of how the specific algebra concept they are learning is used in careers their interested in, using different media. Then, students can create any sort of scenario they want about how the algebra concept is used in the career. One thing we rate is students' originality - whether they come up with a brand new application of math to their career, or whether they closely mirror the examples. Most change at least some key elements of the stories to better fit their interest and experiences. However, we have not seen evidence thus far that it is particularly bad to mirror the examples we give them when writing their own story - they can learn from that too! So far, students have a really hard time getting started writing their very first story about their career, but after that, they do really well on the tasks. There seems to be another kind of drop-off when we reach harder functional forms (e.g., e^x functions), as these functions are harder to apply to the real world in a transparent way that makes clear how they work! Anyways, let me know what other things you're wondering about, and I would love to hear more about your dissertation work!
Ateng' Ogwel
Adem Ekmekci
Great work, Candance et al.! The part I loved the most is the videos of career experts talking about how they use algebra in their work.
What one of the students in the interview said about utility value made think about expanding the work on utility value about a specific content area (math, science) by drilling down to the topics within each subject. This could be studied with students and people from the STEM workforce. This may lead to dramatic revisions in the curricula, or at least, boost the conversations around it.
Kimberly Elliott
Mike Vargas
Matthew Bernacki
Candace Walkington
Associate Professor
Hi Adem, thank you for the comments! We definitely have found the the secondary math curriculum is NOT well-aligned with the mathematics that STEM professionals actually use. It was really shocking for us in the first two years of the grant to discover this. We are teaching students a large set of somewhat useless skills that lay the groundwork for more skills that they probably won't use. There definitely are a small subset of people in academic, research, and technology development positions that use a lot of advanced mathematics including algebra and calculus - but the "everyday" STEM professional seems to have very different set of needs. I think these are important conversations to have too!
Mike Vargas
Matthew Bernacki
Assistant Professor
Yes, elaborating a bit on this thread about the potential motivational benefits here. We ask some rather fine grained questions about career interests as a way of probing student interest to inform match and to evaluate (1) whether personalized math learning improves career & math interests (or their convergence) and also (2) whether there are specific career areas or careers in particular for which Personalized Problem Posing is particularly useful. You bring up a third, exciting area where these materials could be agonists for student-generated utility value to promote relevance. We know from achievement motivation research (Hulleman, Kosovich, colleagues, mid 2010s) that self-generating connections is crucial to generating utility value. These problem posing activities implicitly promote relevance generation, and a good match with relevant examples can be a catalyst. We'll soon conduct analyses to look at the relevance students do (/not) perceive when they engage, and how their interest in math may change as a result. Stay tuned :)
Thomas Smith
Professor
I also love both the videos of scientists talking about the value of algebra and the writing of the algebra stories! What do you see as the learning outcomes of the ASSISTments platform? How do you measure them? What do you think might be some of the challenges of taking this platform to scale?
Neil Heffernan
Professor and Director of Learning Sciences and Technologies
I like Candace's answer about what she is using for her dependent measures so I will let her answer for that but let me say something about scale.
Because the system is ASSISTments, if it beats the traditional method, it would be very easy to scale to the 500,000 students that use ASSISTments. I see great value in more researchers using platforms to do their studies so if they work our the scaling can be done more easily. WPI and the ASSISTments Foundation allow other researchers to propose studies. See https://www.etrialstestbed.org/
Candace Walkington
Associate Professor
Thanks for the comments Thomas! Our platform really focuses on students making meaning of symbolic representations in algebra - in understanding the different parameters and variances in a function equation, in terms of a meaningful real world situation. We want students to be able to take equations apart, and them put them back together again as they think through their own stories. We are measuring their learning through the characteristics of the algebra stories they write, their ability to solve their algebra stories and other algebra stories about their career successfully, and their performance on rep-/post- algebra assessments administered before and after the intervention. We are currently working to scale the platform. Our biggest challenge at the moment is getting it to work on any computer in any browser, regardless of the school's settings. Being located in ASSISTments helps a lot with this, but we use some capabilities outside of ASSISTments to make the platform more interactive.
Mike Vargas
Israel Ramirez
This is a great project, indeed. I have observed throughout the years that most students have a difficulty identifying how algebra can be applied to their careers. It is interesting to see how you engage students to think and write their own algebra parameters to amke career connections. It would be great to find out if there is any communication with any school district in the U.S.A. regarding this project to perhaps improve the algebra curriculum int the middle school and high school level?
Candace Walkington
Associate Professor
Thanks so much for your question! We are really interested in connecting with districts, especially those with schools that use "career academy" type models. This is a great way to make math experiences more personalized within such a model. We are currently working with two districts in North Carolina, and are at the beginning stages of forming a partnership with two districts in California and one in Texas to scale up the use of the platform. It took a long time to build everything, so we are just now starting to focus on scale-up!
Israel Ramirez
Thank you for sharing this amazing project. I'd love to see all my students realizing that math is everywhere. I agree, it would be a great idea to bring this project to schools that use career academy structures. It will benefit both the schools, but most importantly the students. Thank you for sharing!
Mike Vargas
Physics Teacher
I wish we had a lot more folks doing this kind of work. The student ( maybe he graduated) comment " I don't even know what a log does anymore" is so true and on point. As a high school teacher, we struggle trying to explain to kids every day why and where they will see this kind of math again. I know our algebra teachers have a really hard time connecting the dots. Most times they are so focused on passing the test, they forget to explain the why. How many folks are using this platform now and how can I get my hands on it? Great Video
Kimberly Elliott
Candace Walkington
Associate Professor
Thank you so much for your comments Mike! The person who made the comment about log is a practicing mechanical engineer who manages tanks for the military. He said that most of the more advanced math he used was only really relevant when he was taking the professional engineer exam. We are really interested in thinking about what from algebra is useful and compelling in the world of work.
Right now, we are transitioning from small scale use to using the activities at scale. We are planning to develop a new version over the next 6-8 months that is more stable across platforms - but right now, you can access our current version in the free ASSISTments program. Instructions are located at http://bit.ly/algebraforwork. Thanks again!
Kimberly Elliott
Rebecca Vieyra
Doctoral Student
Dear Team,
This is SOOO awesome! This project beautifully integrates career aspirations, content knowledge, and personal relevance. I'd love to see this done across multiple disciplines (also including my own field, physics). It also feels as though it is something that could be fairly easily adoptable by teachers, but not so "off the shelf" that there is no room for student creativity. I also want to commend you for the interface that allows teachers to assign these problems to each other and promote collaboration.
I would love to see you all publish this in some kind of practitioner journal, present at conferences, etc. Have you had this opportunity?
The above question leads to another question for me -- What level of interaction have you had with regard to teachers' involvement as co-researchers or co-designers (if applicable), or what kinds of supports have you been able to provide to teachers beyond the technology itself?
Matthew Bernacki
Candace Walkington
Associate Professor
Hi Rebecca! Thanks for the awesome questions. We recently presented at NCTM and AERA, and have upcoming presentations at NCTM and ASEE. I think a practitioner article would be great for this work too! We spent so long building everything that we haven't been super focused until recently on "getting the word out."
We co-designed with teachers throughout the process - and included middle school high school, community college, and university math teachers. All of these teachers see algebra and its connection to the world of work from different perspectives, so it has been super interesting. We have training materials for teachers that we've used for our studies, but are currently working on putting together videos of the implementation of the activities, and of teachers leading discussions of students' work on these activities, that we will be publicly sharing. I think it's really powerful to see how the teachers are able to support students in overcoming obstacles in understanding the mathematics in the environment!
Rebecca Vieyra
Doctoral Student
Candace,
Having videos of teachers in action will be great -- it's something that I think teachers regularly request, and it captures so much more than what can be transmitted in a lesson plan. Good luck, and keep up the great work!
Mike Vargas
Elizabeth Adams
Great work, Candace and team! I really like how you collaborated with industry professionals to design the learning experiences. We as K-12 practitioners and researchers need to keep evolving as our students' future careers evolve and change.
Mike Vargas
Candace Walkington
Associate Professor
Yes the industry professionals' ideas about how and when mathematics was useful were SO interesting and unexpected! I really want to dig into this more in the future.
Mike Vargas
Physics Teacher
I think you have touched on something in one of the above comments. I don't think folks realize just how much disconnect there is in Math instruction in high school. I would love to see this project scaled up to an entire high school math curriculum from freshman to senior math. Is this something you guys are thinking about? What kind of resources would it take to make something like this happen?
Candace Walkington
Associate Professor
Thank you for this comment! It really gets to the heart of something I have been thinking a lot about. I think we could develop a high school curriculum around the kinds of algebra that are actually useful in the world of STEM careers, and I have thought about building out something to do that. But I don't think anyone would use it, because it would not be aligned to the standards (e.g., I have yet to talk to a STEM professional who uses the quadratic formula), and it would also not cover all the prerequisite knowledge needed for courses like calculus. I have been thinking about who we would need at the table, on a team, if we were going to reimagine the secondary mathematics sequence and how it leads into college level mathematics, as a sequence that is relevant to how math is actually meaningfully applied to the world of work and to social issues. The level of change that this reimagining would require of the system is staggering. But I am interested in thinking through what those first steps are!
Brooke Istas
Brooke Istas
3rd year Ph.D. Student
Mike,
I couldn't agree with you more. As a practitioner at a community college, students are always questioning the application of College Algebra. One of the biggest take-aways for me in this project is that much of the math that is taught is not used in STEM careers' everyday work. It causes me to think as a practitioner why am I teaching something that does not add to a learner's trajectory? Would that time spent teaching useless concepts be better utilized if the curriculum's focus shifted to a more in-depth understanding of the tasks that are used in STEM fields?
Mike Vargas
Mike O'Brien
What a fantastic idea, and what excellent video. I'm proud to have Elizabeth Leyva on our faculty.
Candace Walkington
Associate Professor
She has been such a huge asset to this team!
Mike Vargas
Physics Teacher
Candace and Brooke -
From my position here, I am seeing this shift in thinking starting to take place...... I think you have the mojo if you wanted to full court press on your project and get lost of support from other "other friends" I think you are wrong -but in fact would have a large amount of schools that would use it. I have already started hearing rumbling of shifting how we execute math education to a more "user friendly" model and I think you could very easily poise yourselves to be on the ground floor of something big. If that means changing the metrics? So be it? Maybe now is the time....
Brooke Istas
Candace Walkington
Candace Walkington
Associate Professor
Thanks for the encouragement! I think we are in a unique moment right now to reimagine what secondary math could be!
Brooke Istas
Brooke Istas
3rd year Ph.D. Student
And post-secondary math, too.
Susan Warshaw
This idea is long overdue. Hope it catches on!
Brooke Istas
Mike Vargas
Candace Walkington
Associate Professor
Awesome, thanks Susan!
Jeremy Roschelle
Hi Candice and team, I liked this new use of ASSISTments -- how you center on 'function' makes sense, the connections to the real world make sense, and I really liked the scaffolded activities where students end up making their own stories. Would love to get a copy of your RCT results when available -- put me on the list :)
Brooke Istas
Candace Walkington
Matthew Bernacki
Candace Walkington
Associate Professor
You are definitely on the list ;-) We should be putting together some preliminary results for an AERA submission this summer - I hope. Thank you for your support of our research!
Brooke Istas
Further posting is closed as the event has ended.