1. Maria Blanton
  2. https://www.terc.edu/display/Staff/Maria+Blanton
  3. Senior Scientist
  4. Project LEAP: Extending a Grades 3-5 Early Algebra Learning Progression into Grades K-2 (IES) and Building a Grades K-2 Early Algebra Learning Progression Prototype for Diverse Populations (NSF)
  5. https://www.terc.edu/projects/project-leap/
  6. TERC
  1. Angela Gardiner
  2. https://www.terc.edu/profiles/angela-murphy-gardiner/
  3. Senior Research and Design Specialist
  4. Project LEAP: Extending a Grades 3-5 Early Algebra Learning Progression into Grades K-2 (IES) and Building a Grades K-2 Early Algebra Learning Progression Prototype for Diverse Populations (NSF)
  5. https://www.terc.edu/projects/project-leap/
  6. TERC
  1. Ana Stephens
  2. https://wcer.wisc.edu/About/Staff/1213
  3. Researcher
  4. Project LEAP: Extending a Grades 3-5 Early Algebra Learning Progression into Grades K-2 (IES) and Building a Grades K-2 Early Algebra Learning Progression Prototype for Diverse Populations (NSF)
  5. https://www.terc.edu/projects/project-leap/
  6. University of Wisconsin Madison
Public Discussion

Continue the discussion of this presentation on the Multiplex. Go to Multiplex

  • Icon for: Maria Blanton

    Maria Blanton

    Lead Presenter
    Senior Scientist
    May 9, 2022 | 05:20 p.m.

    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?

     
    1
    Discussion is closed. Upvoting is no longer available

    Alejandra Duarte
  • May 10, 2022 | 09:50 a.m.

    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! 

  • Icon for: Angela Gardiner

    Angela Gardiner

    Co-Presenter
    Senior Research and Design Specialist
    May 10, 2022 | 10:15 a.m.

    Thanks, Cassandra.  

  • May 10, 2022 | 11:31 a.m.

    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. 

  • Icon for: Ana Stephens

    Ana Stephens

    Co-Presenter
    Researcher
    May 10, 2022 | 11:51 a.m.

    Thanks, Eva! Yes, would love to connect! One challenge I see is that real-world data/issues are often messy whereas when our young students first encounter (for example) functions, their "data" are perfectly linear (or quadratic, or exponential). But seeing math as a tool to describe the real world is so important.

  • Icon for: David Kung

    David Kung

    Facilitator
    Director of Policy
    May 10, 2022 | 11:57 a.m.

    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?

  • Icon for: Angela Gardiner

    Angela Gardiner

    Co-Presenter
    Senior Research and Design Specialist
    May 10, 2022 | 01:58 p.m.

    Thanks for your questions David, and thanks for watching.

    How are the lessons and interactions structured to address EDI issues? 

    We worked with different advisors to develop a curriculum that was culturally and developmentally appropriate.  We tested this curriculum in several settings both in schools with low SES status and in schools with high percentages of students with learning differences.  We incorporate discussion and manipulatives in ​all our lessons, which we have found help students who have learning difficulty in math.   We have included a section in our curriculum which provides strategies for teachers to support struggling learners. This was developed ​with the help of several advisors who have extensive research experience on students with learning differences, as well as from teachers who work with a variety of students every day in their classrooms.

    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?

    In a large-scale, randomized study we found that students who took our Grades 3 – 5 intervention as part of their regular instruction were significantly more prepared for algebra than those who had only their regular curriculum. These findings held for students from schools with 100% low SES status and 90+% students of color.

    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?

    We haven't researched this area, but I can see the connection as well. It would be interesting to look into.

  • Icon for: Myriam Steinback

    Myriam Steinback

    Facilitator
    Consultant
    May 10, 2022 | 01:24 p.m.

    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?

  • Icon for: Angela Gardiner

    Angela Gardiner

    Co-Presenter
    Senior Research and Design Specialist
    May 10, 2022 | 01:42 p.m.

    Thanks for watching, Myriam.  This is such a fun age group to work with.  The 18 lessons are used throughout the school year, teachers teach approximately 1 lesson a week and each lesson ranges from 30 mins to 1 hour depending on grade level (K-2 is 30 mins a lesson).  Teachers we have worked with have found this very doable with their regular math curriculum.  Professional development is available, and we do recommend it.  We have worked hard, however, to make sure the lesson are easy for teachers to follow and understand because we realize not all districts have time or can afford PD.  In the future we would like to incorporate a suite of videos that would be accessible to teachers who can't participate in the PD, but would like a little more information before beginning a lesson in their classroom.

     
    1
    Discussion is closed. Upvoting is no longer available

    Myriam Steinback
  • Icon for: Meixia Ding

    Meixia Ding

    Higher Ed Faculty
    May 11, 2022 | 05:58 p.m.

    Thank you for sharing this exciting project! It is very encouraging and impressive to see the figure that shows the performance difference between the intervention and the control groups! I also have a question about the intervention (18 lessons). It looks like these 18 lessons were added as extra materials to the regular math curriculum for the intervention group, right? How did you deal with the factor of content exposure? In other words, has the intervention group received 18 more lessons than the control group? Did I have a misunderstanding here? 

  • May 10, 2022 | 02:50 p.m.

    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!

  • Icon for: Angela Gardiner

    Angela Gardiner

    Co-Presenter
    Senior Research and Design Specialist
    May 10, 2022 | 03:01 p.m.

    Thanks Leanne.  I am familiar with your project, and viewed your video earlier today, job well done!.  I also see a connection, maybe our paths will cross in the future.  We have been tinkering with the beginnings of an EA digital assessment tool, we may need connect down the road.  Thanks again for checking our work out!

     
    1
    Discussion is closed. Upvoting is no longer available

    Ana Stephens
  • Icon for: Noelani Ogasawara Morris

    Noelani Ogasawara Morris

    Facilitator
    Demonstration Teacher
    May 10, 2022 | 11:24 p.m.

    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?

  • Icon for: Angela Gardiner

    Angela Gardiner

    Co-Presenter
    Senior Research and Design Specialist
    May 11, 2022 | 08:48 a.m.

    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.  

  • Icon for: Noelani Ogasawara Morris

    Noelani Ogasawara Morris

    Facilitator
    Demonstration Teacher
    May 11, 2022 | 12:53 p.m.

    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!

     
    1
    Discussion is closed. Upvoting is no longer available

    Angela Gardiner
  • Icon for: Janet Stramel

    Janet Stramel

    Researcher
    May 11, 2022 | 09:31 p.m.

    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?

  • Icon for: Angela Gardiner

    Angela Gardiner

    Co-Presenter
    Senior Research and Design Specialist
    May 12, 2022 | 07:33 a.m.

    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.

  • Icon for: jennifer Knudsen

    jennifer Knudsen

    Researcher
    May 12, 2022 | 11:03 a.m.

    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?

  • Icon for: Ana Stephens

    Ana Stephens

    Co-Presenter
    Researcher
    May 12, 2022 | 11:24 a.m.

    Thank you, Jennifer! One change was that we used more hands-on activities in the younger grades, including the use of balance scales to model mathematical equivalence and Unifix cubes to model even and odd relationships and arithmetic properties. We also see perhaps even more connections to traditional arithmetic goals at this age. For example, as students discover and discuss the Commutative Property of Addition, they are simultaneously working on arithmetic skills. They later put these properties of operation to use to compute more efficiently (e.g., when thinking about how to compute something like 9 + 5 - 5).

  • Icon for: Cynthia Orona

    Cynthia Orona

    Program Coordinator
    May 12, 2022 | 02:25 p.m.

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

  • Icon for: Ana Stephens

    Ana Stephens

    Co-Presenter
    Researcher
    May 12, 2022 | 02:34 p.m.

    Thanks for visiting, Cynthia! I just watched your video and enjoyed it as well!

  • Icon for: Peter Tierney-Fife

    Peter Tierney-Fife

    Senior Curriculum/Instructional Design Associate
    May 12, 2022 | 02:30 p.m.

    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!

  • Icon for: Ana Stephens

    Ana Stephens

    Co-Presenter
    Researcher
    May 12, 2022 | 02:57 p.m.

    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.

  • Icon for: Peter Tierney-Fife

    Peter Tierney-Fife

    Senior Curriculum/Instructional Design Associate
    May 12, 2022 | 04:55 p.m.

    This is helpful, thank you. I share your thinking that use of visual representations helps all students, including students who are multilingual. My work includes thinking about ways visual representations (right now, mostly diagrams like single or double number lines and tape diagrams) and receptive and productive language strategies can be combined in activities for mathematics teacher professional learning, and I appreciate your information on combining visuals with gestures, acting out, and careful vocabulary work with students in LEAP. Thanks again.

     
    1
    Discussion is closed. Upvoting is no longer available

    Ana Stephens
  • Icon for: Maria Blanton

    Maria Blanton

    Lead Presenter
    Senior Scientist
    May 16, 2022 | 09:15 a.m.

    Thank you Peter. Visual and concrete representations (and gestures!) have been key to helping young children in our study understand algebraic ideas. It's fascinating how particular tools can challenge their thinking about "simple" concepts like the equal sign and help them begin to think algebraically. I'm curious about double number lines and tape diagrams and how you use these. Do you have a reference you can share? I thoroughly enjoyed your video. One of the delights of our work - which I appreciated in your video as well - is talking to young learners and listening to their thinking and ideas. They always have wonderful insights to share!

  • Icon for: Peter Tierney-Fife

    Peter Tierney-Fife

    Senior Curriculum/Instructional Design Associate
    May 16, 2022 | 01:08 p.m.

    Maria, I agree it is a delight to talk with young learners, and I think a responsibility to listen well to their thinking and ideas. The most available resources I can share are from a different project, Visual Access to Mathematics (if interested, see our old video on the multiplex which has some context and resources in comments). It's focused on grades 6–8, ratio and proportional reasoning. We also have some example activities online and, for use of double number lines in percentage contexts, there are more resources associated with this collection of percentage change apps. One of my favorite sets of resources makes connections between double number lines and the coordinate plane and includes this Double Number Line to Coordinate Graph app.

  • Icon for: Maria Blanton

    Maria Blanton

    Lead Presenter
    Senior Scientist
    May 17, 2022 | 09:41 a.m.

    Great - thanks for the resources Peter!

  • Icon for: Zach Mbasu

    Zach Mbasu

    Informal Educator
    May 14, 2022 | 05:01 p.m.

    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?

  • Icon for: Maria Blanton

    Maria Blanton

    Lead Presenter
    Senior Scientist
    May 16, 2022 | 09:04 a.m.

    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! 

  • Icon for: Carol Lumm

    Carol Lumm

    May 16, 2022 | 10:27 a.m.

    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.

  • Icon for: Maria Blanton

    Maria Blanton

    Lead Presenter
    Senior Scientist
    May 16, 2022 | 10:34 a.m.

    Thanks so much Carol!

  • May 16, 2022 | 01:02 p.m.

    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!

  • Icon for: Maria Blanton

    Maria Blanton

    Lead Presenter
    Senior Scientist
    May 17, 2022 | 09:42 a.m.

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

  • To post to this discussion go to