Welcome! This video provides an overview of findings from the first three years of a large-scale longitudinal study. As described in the video summary, we implemented an early algebra instructional sequence in grades 3-5 and tested the impact of this intervention on students' growth in algebra understanding as compared to a business-as-usual control condition. The students who participated in this study are now finishing up grade 6 and are again being assessed so that we can continue to examine and compare growth in algebra understanding one year post-intervention.

 

Do you have experiences as a teacher or researcher engaging elementary students in algebraic thinking? Where in the elementary math curriculum do you see opportunities to engage students in such thinking? What success stories or challenges would you like to share?

 

Do you have experiences as a teacher or researcher engaging secondary students in algebraic thinking? Where do you see successes and where do you see challenges? Are there particular algebraic concepts with which you see students struggle that perhaps could be introduced in the context of early algebra?

 

Thanks so much for watching our video and contributing to the discussion!

This is a very interesting project! As a former 8th grade Algebra teacher I am all too familiar with students who would struggle with basic algebraic concepts. I am curious whether you find the barrier to be more with the language and understanding of vocabulary or with the application and ability to reason within/higher order thinking? At a younger age, I imagine it could be a combination of both?

Hi, Courtney. Good question. In the early grades, students do learn some vocabulary (e.g., "conjecture," "variable," and [function] "rule"), but this vocabulary is introduced gradually and in context and repeated and practiced often. We don't expect elementary students to talk about "polynomials" or use overly complex language. The same can be said for the concepts. We focus on a few big ideas as outlined in the video and really spend time developing them. We are interested in laying the foundation so that by the time these students reach 8th grade algebra the more formal mathematics makes sense. Thank you for watching!

Hi Maria! As you look at developing students' growth in the Big Algebra Ideas - Expressions, Equations, Equality & Inequality, Functional Thinking, and Generalized Arithmetic - how do you think about the sequencing and connecting these ideas through the development? Is it more of a building from one to the other or spiraling through the big ideas?

Similarly do you see Thinking Practices as being evident through the development of each Big Algebra Idea?

Lastly what do the students think about learning algebra and mathematics in this way?

Maria et al., Thanks for an enticing summary of this project and for ll you have been doing to advance student mathematical understanding. As this is a quite large study, I expect that you will have the statistical power available to detect the kinds of pre- and post-intervention effects you described briefly. What other outcomes and impacts do you have planned to investigate and how fine-resolution will the data be in terms of picking apart individual student factors and the effects of the intervention? 

Hi Maria,

I currently teach 8th grade Algebra, Pre-Algebra, and Geometry and most certainly see the importance of introducing algebraic thinking at an early age.  The results that you have found so far are great and I look forward to seeing what happens with the results as the levels of math continue to increase. The students that I teach that generally struggle with math often have trouble with comprehending word problems in our pre-algebra course.  For instance when we teach rate of change our students often struggle with applying the algebra content to the real world and struggle with seeing slope through multiple representations, whether it be a graph, table, or equation.  Do you predict that the group of students that have been introduced to this program will be able to take an application problem in an algebra course and can accurately make connections across multiple representations?  Additionally, are you looking at the impacts of this program with students that may have learning disabilities?  

I am interested in finding out more about the PD development that you put in place in order to help build these algebra foundations.

Thanks!

 

Hi Nicole, 

Thanks for your question.  My name is Angela Murphy Gardiner and I am a teacher and researcher on Project LEAP.  In grades 3-5 we do multiple problems in the functional thinking domain.  Within these lessons students are introduced to real world problems and represent the data in multiple ways (function table and graphing).  Students are doing really well in this area.  They are able to graph and make interpretations based on their graphs and tables.  This of course is the early stages, but we believe this is setting them up to be very successful when they get to you and discussions about slope really begin to take shape.  

As for the PD, we met with teachers for a day in the summer to introduce them to early algebra big ideas and key practices.  We then met with them for a half day monthly (September-April).  During these sessions we walked them through each of the lessons they would be teaching and provided them opportunities to solve the problems on their own, ask questions about the problems and we showed them classroom videos so they could see how elementary students think through the problems.  I was also available to teachers via phone or email if they had any questions between our meetings.  We did our best to provide as much support as possible for our teachers.

We have a new project that we are in the early stages of, working with students in K-2.  This project focuses on students in culturally diverse districts and students with learning disabilities.  We will have data on this in the coming years, and it is a project we are very excited about.

Thanks again for your questions.