From the Project LEAP team, thank you for taking a moment to view our video! We are excited to share this final stage of our work designing an effective early algebra intervention for elementary grades. We look forward to answering your questions during this Video Showcase. We would be glad to share more about our intervention, how it improves students’ algebra readiness, and how you can get the LEAP curriculum in your schools. Something to think about:

What are your experiences with early algebraic thinking?

If you are a secondary mathematics educator, what are some of the challenges your students face that might be addressed in the earlier grades?

This is really exciting work and related to our numeric relational reasoning formative assessments! Supporting teachers with instructional decisions and then intervening with high quality lessons to support algebraic thinking are so critically important! Exciting work! 

Ana great video ... thanks for sharing your work and checking out ours. I would love for us to connect about how to leverage each others' work. 

Love seeing how algebraic thinking is appropriate - even vital - in early grades! 

The attention to equity is admirable – but it only got a brief mention in the video. How are the lessons and interactions structured to address EDI issues? 

Absent longitudinal data, what does evidence look like to suggest these students will fair better when they get to later, middle- or high-school Algebra I classes?

The picture of balances make me wonder if kids are also building early physics knowledge. Is there anything in the literature about concepts of levers and torque in such early learners?

How great that you are able to bring LEAP to K-2! Young students are able to have algebraic ideas - if we get away from the 'x and y' mindset - and your design shows that. I wonder about the 18 lessons - how and when are they designed to be used? What support, if any, do teachers need to facilitate the lessons?

Such interesting work! Connecting algebra learning to the K-2 classroom is so important. We are developing classroom assessment resources that tie in some of these early numeracy concepts that focus specifically on numeric relational reasoning. I see a lot of useful cross-overs with your intervention. So excited to see where this work goes. Thanks for sharing!

I completely agree that introducing the concepts of algebraic thinking and developing relational thinking across the equal sign is so valuable at the early elementary grades.  I notice that the LEAP program uses a variety of tools and what appears to be guided strategies for problem solving.  Is there room and flexibility  for students to use their own strategies to problem solve and share their thinking to their classmates?

Hi Noelani,

Great question!  The answer is YES!, we encourage a wide range of discourse and encourage children to share their math thinking and strategies in every lesson.  We discuss with students, on a regular basis, that there are often multiple ways to solve a problem, and we share as many as possible.  LEAP discussion is also student driven, so often students present the ideas or solutions and discuss with each other in whole group meetings.  I believe the algebraic thinking concepts are important, but math discussion in elementary classrooms is also VERY important, and often doesn't happen enough. We try to highlight the importance of math discussion throughout the curriculum and when we work with teachers.  

Wonderful- I love hearing about educators who value, if not more, the process of problem solving versus the final answer.  While efficiency and accuracy are definitely important, building that number sense and flexible thinking in the early years are so valuable in their lifetime as mathematicians!

I LOVE that you are teaching algebra with the elementary students. I have found that some people (even children) are afraid of the word "algebra." Do you tell them they are doing algebra and just doing the math?

Hi Janet,

I agree that people are afraid of the word algebra.  When we did our grades 3-5 intervention we spoke with students about how the math they were doing was the beginning stages of algebra, and the children LOVED it!  They would go home and tell their parents they were doing algebra and work with older siblings on algebra homework, they thought it was a BIG deal.  We don't mention it at the K-2 level as much, and really the work we are doing with these students transcends all types of math.  We encourage them to use the strategies we teach them in  LEAP lessons in all their math work, we don't want the focus to be "we do this type of math when we do LEAP or algebra".  Thanks for taking and interest in the video, and for this great question.

Great project and video! When you show what the K-2 students can do, it's amazing! What was it like to move down to that grade level from g 3-5?

Thanks for sharing!  I totally agree with the need to teach algebra in the early, formative years.

Thanks so much for sharing this work—it's very important and exciting! I am wondering if you can share more about the student-driven discussions and the approaches or resources you use to help students build their communication skills and support their discussions.

Your approach seems to include rich problems/activities with a lot to talk related to them, which is great. I'm wondering more about particular language strategies or discussion aids, and most specifically, I'd love to know if you have particularly effective or favorite approaches to support students who are multilingual learners in English language mathematics classrooms.

Thanks in advance!

Thank you for this important question. We don't have all the answers, and I hope we can learn from others here (I just watched your video and love the focus on students' mathematical strengths--it makes me think about broadening the definition of "good at math.") I will share that we think our focus on visual representations helps all students, including multilingual learners. We model mathematical equivalence with balance scales. We use visual representations of even and odd numbers using dot cards (seen in the opening scene of the video) and Unifix cubes. We also model arithmetic properties (e.g., the Commutative Property as seen in the video) with physical materials.

We do also focus on particular vocabulary. For example, as early as Kindergarten we discuss with students the meaning of "conjecture" and "argument" and revisit these meanings throughout the lessons as we ask them to make and test conjectures. We talk about even and odd numbers in terms of "pairs" and "leftovers" and spend some time "acting out" these ideas. For example, students might be asked to figure out if there is an even or odd number of students in the class without counting. We also talk explicitly about the meaning of the equal sign--often replacing the equal sign with "is the same as" when we read equations--and use gesture when talking about "balance" in equations and the "sides" of equations.

When kids understand Algebra other challenges go down! This is an amazing Algebra intervention and I would definitely want to learn more. In my country there are challenges that remain, particularly in the area of equity and equality. I am wondering how can I provide this kind of learning to girls and boys in remote, rural, and hard-to-reach areas in Africa that have no access to teachers?

Hi Zach - thank you for stopping by! We totally agree that algebra is so central to mathematical success! Feel free to email us for more information about the intervention. We'd be happy to talk further. We have a companion intervention for Grades 3 - 5 which we developed prior to our K - 2 work. We found that students from marginalized communities who had this intervention as part of their regular curriculum significantly outperformed peers in similar demographic settings who had only their regular curriculum. So we know this approach is effective for all students! You describe a difficult challenge, but we would be happy to talk more. Also, I wanted to say I loved your video. It is truly amazing how students around the world can connect and learn with and from each other! 

Congratulations Maria, Angela and the rest of the LEAP team.  Very informative video and I'm enjoying following the discussion of your work.  Thanks for your contributions to the important topic of introducing young students to algebraic thinking.

This is great! I love hearing about these early introductions to algebra. I use algebra everyday in the "real" world. It's so important kids learn the skills early and then understand how critical the skills are in everyday life. Thanks for your work!

Thanks so much Abigail! We agree that this is so important for young learners. Thanks for stopping by!