Tracking the Thinking Process

There are a record number of students performing below grade level in math, and at the same time, critical staff shortages are affecting schools’ abilities to service all students who need support.  The CRA and VRA approaches are highly successful pedagogical methods that have potential to positively impact students in RTI Tier 1 instruction, but currently have two inherent limitations to scale beyond small group settings: efficiency and accessibility.

The CRA approach gained popularity as an instructional method benefiting students with learning disabilities, intellectual disabilities, or autism. However, research shows that students who struggle in math and those with a successful history in math also benefit from the structured and multisensory design of the CRA approach (Witzel, 2005; Bouck, Satsangi, & Park, 2018). The VRA approach solves most issues of accessibility.  With a single device and internet connection, students can access any virtual manipulative that exists in the physical classroom and can gain access to read-alouds, videos, and other accommodations. Virtual manipulatives have evidence of being effective both with students with disabilities (Bouck & Park, 2018; Park, Bouck, & Josol, 2020) and in elementary math classrooms (Rich, 2021). However, an issue of efficiency still exists with current tools in the virtual manipulative market.  Even when students are engaged in live, explicit instruction and teachers can see all student screens in tandem, they still don’t have the ability to critically analyze every students’ movements simultaneously. This inefficiency limits scalable CRA and VRA method utilization by teachers for Tier 1 instruction and leads research in the direction of studying its impact mostly in small group settings.  

Uplift K12 has many components that were built upon the CRA framework. The most significant innovation informed by CRA is that Uplift K12 substitutes concrete manipulatives for virtual manipulatives, allowing for digital breadcrumbs on each interaction that students make on the platform.  A guest student answers an assigned math activity through a shared link for independent practice.  As the student completes a multi-step activity, the student has the opportunity to move objects virtually, such as a number line or place value blocks, watch a video with explicit instruction, or listen to a read-aloud of the instructions and problem. Students can also utilize a drawing toolbar and whiteboard space for virtual representations of the manipulatives on the board.  Data from each interaction, whether a click, drag, type, or submit is silently captured in the form of xAPI statements to a database. When students invite other students to their board, data on each student’s interactions are grouped in an activity under the same session. However, the focus of the new tool is not only to assess whether the student correctly identifies an answer. It is meant to collect all interaction data (i.e. process) that led the student to their particular response (i.e. outcome). The data that is extracted from every learning task would compile in a database without personally identifiable information and would be available to the public and accessible by API key for further research for the purpose of flagging misconceptions in real-time and interpreting collaborative efforts by students in solving math problems.

This approach prevents teachers from intervening in real-time classwork. The proposed data collection mechanism will tell a story of the thinking process in both text-based and visual format. In contrast to the current tool, each activity question can extract many lines of data that can be translated as a story:
On the first place value activity, objective 3.OA.1, Student 1:
● incorrectly dragged the tens block to the hundreds place 3 times at 8:20AM.
● correctly dragged the ones block to the hundreds place 9 times at 8:21AM.
● incorrectly submitted “39” with target “309” at 8:22AM.
● clicked accessibility tool- video at 8:22AM.
● clicked accessibility tool- read-aloud at 8:25AM.
● correctly dragged the tens block to the tens place 3 times at 8:26AM.
● correctly dragged the ones block to the hundreds place 9 times at 8:27AM.
● correctly submitted “309” with target “309” at 8:28AM.
● clicked next question button at 8:28AM.
The newly-added data also includes a screenshot, which can be utilized to supplement the text-based story with visual evidence. The event listeners could potentially “watch” students make multiple interactions on an activity, without their physical presence at a particular time.

Unfinished learning from Covid-related school shifts is pervasive and inequitable. While most students experienced some form of unfinished learning, students of color fared the worst.  Students in majority-Black schools were on average, 2 months behind in math than students in majority-White schools, and overall, students in low-income communities fared significantly worse than students in suburban communities (Curriculum Associates & McKinsey, 2021).  Schools have the daunting task of catching students up but are also experiencing high staff turnover rates and shortages.

Uplift K12’s proposed tool provides freemium access to activities, videos, and a learning platform that enables explicit instruction.  Explicit instruction in mathematics is considered effective for a wide range of students, including students with and without learning disabilities and students with moderate to severe developmental disabilities (Bouck & Sprick, 2018). By increasing the likelihood of effectiveness of Response to Intervention (ie, RTI)  Tier 1 interventions, Uplift K12 can positively impact students’ inclusivity and belongingness in the math classroom. If successfully scaled, Uplift K12 will reduce the number of students who require more costly and resource-intensive supports as recommended by RTI Tiers 2 and 3. Students with IEPs, or Individualized Education Programs, who require accommodations in the form of manipulatives, read aloud, or increased text size, can access the Uplift learning platform by clicking on an invite link sent from a free teacher account.  

Uplift K12 is currently working with 5 school districts in Texas. We have provided virtual and in person professional development trainings at these schools. During these trainings we spent time hearing teacher feedback. Using that feedback we went back to our technology team who changed and added features that best supported the feedback we received from teachers. We plan to grow significantly this year by adding a freemium model to our existing top-down approach with schools.

Mehul Shah, Michelle Shah, and Juan Gatica are members of the executive team at Uplift K12. The team also consists of 4 formal advisors, including 3 academic researchers.

 Mehul taught for 10 years in low performing schools and low income communities. His focus was on math intervention and helping students catch up to grade level and build math confidence using manipulatives. He then transitioned full-time into product management and front-end web development before co-founding Uplift K12 with Michelle.

 Michelle was a Montessori-certified teacher, who worked in public school settings for 10 years. Her experience focused on the early grades of Pre-K 3 to kindergarten. Michelle now focuses on curriculum design and operations as a co-founder for Uplift K12.

 Juan is a highly successful former Principal of over 25 years, currently manages school partnerships, and is an equity partner of Uplift K12.

 Advisors: Dr. Brad Witzel, Dr. Emily Bouck, and Dr. Yan Ping Xin are researchers and current professors at their respective universities WCU, Michigan State University, and Purdue University.  They contribute to the development of Uplift K12 curriculum and accessibility design. Ashish Trehan is an experienced data scientist who has worked for top consulting and accounting firms and formally advises the design of Uplift’s data and reporting features.

Evidence on why UpliftK12, as a complete product, will positively influence math learning is presented in this section. The proposal is funding the data collection mechanism for this product, details of which are presented briefly in the section on new tool description and the learning engineering section.

Decades of research supports the use of the CRA and VRA methodologies.(e.g., Agrawal & Morin, 2016; Bouck, Satsangi, & Park, 2018; Butler, Miller, Crehan, Babbitt, & Pierce, 2003; Miller & Mercer, 1993; Underhill, 1977). However, much of this research has included small sample sizes due to the focus on students with disabilities. A notable exception that informed the development of Uplift K12 is one by Witzel (2005). This study focused on teaching Algebra 1 to students using the CRA approach, but unlike dozens of other studies involving the CRA method with small sample sizes, included data from a large number of students (231) with a history of low, medium, and high math achievement. Students, regardless of learning disability status, who were taught through the CRA approach versus the abstract-only fared significantly better on post-test and maintenance (Witzel, 2005).  The study concluded that students taught through the CRA method may develop and remember procedural steps more accurately and make fewer basic computational mistakes than if taught abstract-only.

Other studies corroborate that students not only performed better with virtual manipulatives than concrete, but they also showed preference for the virtual manipulatives, possibly due to the stigma associated with older students using physical blocks to learn middle school math (Bouck, Park, Shurr, et al, 2018; Bouck, Chamberlain, & Park, 2017; Bouck, Satsangi, Taber-Doughty, & Courtney, 2014; Satsangi & Bouck, 2015; Satsangi, Bouck, Taber-Doughty, Bofferding, & Roberts, 2016).

Uplift K12 replicates the methodology of the CRA and VRA approaches by supporting all 4 known steps of the process: demonstration, modeling, guided practice followed by independent practice, and immediate feedback  (Sealander, Johnson, Lockwood & Medina, 2012).  Demonstration and modeling can be completed by videos directed to students or live instruction provided by an educator. Uplift K12 also houses ready-made guided practice and independent practice and allows teachers to provide live feedback to students.  Uplift K12’s use of video modeling for explicit instruction is supported by research. Researchers (Bouck, Park, Shurr, et al, 2018) who studied the influence of CRA intervention with video modeling to support acquisition of addition, subtraction, and number comparison, as well as other mathematical skills in students with autism.  The study concluded that this method, in conjunction with video modeling, was effective. 

After demonstrations and modeling, students should be given opportunities to practice the mathematical model as part of Guided Practice. Eventually, Uplift K12 expects that results from learning engineering research efforts can be applied to the tool so as to allow teachers to conduct Guided Practice with the entire class, in both physical and virtual settings.

For independent practice, Uplift K12 integrates the virtual and representational components of each activity with the abstract, as proposed by research that concludes explicit instruction that involves the use of manipulatives should also include the presentation of the numerical problem (Miller, Stringfellow, Kaffar, Ferreira, & Mancl, 2011).

Current tools share data, but often it is only of the outcomes which may come too little too late or are just too complex. Our solution focuses on collecting real time data of the process and the outcome. We want to share this data with researchers, who will study patterns in student thinking, which will then help better inform teacher instruction.

The actual process of how a student gets to a certain conclusion is not studied. Currently schools focus on collecting data of outcomes, but once it reaches a teachers hand it can be too late to enact any meaningful help or change. At this point a teacher has already had to move on to the next unit to keep up with pacing or worse that student has already moved on to another teacher. 

We believe that if we flip the script and start focusing more on the actual learning process we can create a bigger impact on how a students learning is measured, making high stakes testing less relevant. 

Uplift K12 is currently working with 5 school districts in Texas. We plan to grow significantly this year by adding a freemium model to our existing top-down approach with schools.

Currently, the data we collect is after the student pushes submit. It is limited on many fronts and does not showcase data from multiple students moving manipulatives simultaneously, as a group. But… what data can we gather before they push submit?

During the next year we will be collecting more data that will help us understand the thinking process which in turn  can help us create automated, immediate, and actionable insights for whole group settings.Researchers will receive breadcrumbs from interactions with mouse and keyboard. 

During the next five years, we envision releasing the dataset to researchers in order to encourage more research on using virtual manipulatives. Building a new pathway for research that combines process data with outcome data that will then help educators understand student misconceptions and how individual students learn best.