3976 Views (as of 05/2023)
  1. Madhavi Jayanthi
  2. Director of Research
  4. Instructional Res Group
  1. Joe Dimino
  2. Deputy Executive Director
  4. Instructional Res Group
  1. Russell Gersten
  2. Executive Director
  4. Instructional Res Group
  1. Robin Schumacher
  2. Sr. Research Associate
  4. Instructional Res Group
  1. Samantha Spallone
  2. Research Associate
  4. Instructional Res Group

Intervention for Improving Struggling 5th-Graders’ Fractions Achievement

NSF Awards: 1535214

2019 (see original presentation & discussion)

Grades K-6

We recently conducted a large-scale randomized controlled trial of a fractions intervention for 5th-grade struggling students. The study was conducted in three school districts and included 205 students (102 in treatment and 103 in control) who were between the 15th and 37th percentile on a fractions screening measure. Students in the treatment condition received 35 minutes of fractions intervention 3–4 times a week. The intervention emphasized the use of the number line to teach understanding of both foundational and grade-level fractions concepts. It also emphasized building students’ ability to explain their solution strategies and the underlying mathematical concepts for operations. The post-tests given at the end of the intervention indicated that students who received the fractions intervention outperformed students who did not receive the fractions intervention on a range of measures (effect size [Hedges’ g] of .66 to 1.08; p < .0001).

In this 3-minute video, we will highlight how the number line was used to teach the fractions content and what was done to facilitate student written and verbal explanations. We will also briefly highlight the results.

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Discussion from the 2019 STEM for All Video Showcase (16 posts)
  • Icon for: Susan Jo Russell

    Susan Jo Russell

    Principal scientist
    May 13, 2019 | 12:34 p.m.

    Hi Madhavi,

    Thanks for the interesting video on students' fraction learning--your focus on 4th and 5th graders' fraction understanding is so important.  I was especially intrigued by your focus on students' explanations since current research (e.g., Megan Franke et al.) highlights the correlation of students' giving complete explanations and interacting with each others' explanations with math achievement.  In your study, did students mostly work independently, writing their own explanations, or was there also classroom discourse around students' explanations?  Thanks.

  • Icon for: Robin Schumacher

    Robin Schumacher

    Sr. Research Associate
    May 13, 2019 | 02:08 p.m.

    Hi! Thanks for the question. Students wrote their explanations independently; however, interventionists modeled mathematically accurate and complete verbal explanations and written explanations before students were asked to write their own. Additionally, we provided a self-regulated prompt to help the students move through the process while writing independently. I hope that helps. 

  • Icon for: Samantha Spallone

    Samantha Spallone

    Research Associate
    May 13, 2019 | 12:47 p.m.

    Thank you for taking the time to watch our video! Our research team would be interested in your feedback, especially in regard to the following questions:

    1. Does this video make you want to learn more about instructional strategies in this curriculum?
    2. What did you learn about this curriculum and ways it helps students?
    3. Could you take aspects of this curriculum and apply to your own school? If so, what would they be? If not, why not?
  • Icon for: Sandy Wilborn

    Sandy Wilborn

    Director of Programs
    May 13, 2019 | 05:53 p.m.

    I enjoyed the video.  As a former Pre-Calculus teacher, I know the struggles that students face when it comes to fractions...even at that level.  It is vital that students get a strong foundation in upper elementary school so that they are successful in secondary mathematics.  Thank you for your work!

  • Icon for: Robin Schumacher

    Robin Schumacher

    Sr. Research Associate
    May 14, 2019 | 08:08 a.m.

    Thank you for your nice comment. Fractions are so important for advanced mathematics and our research focus is to address these issues in upper elementary school so that students can be successful. 

  • Icon for: Russell Gersten

    Russell Gersten

    Executive Director
    May 14, 2019 | 10:15 a.m.

    Thanks for the kind words, Sandy. Research  by Bob Siegler and others  does support the importance of truly understanding fractions, especially understanding relative magnitude of fractions in predicting success in algebra and beyond. Important for  more folks to appreciate the insight that you have.

  • Icon for: Denise Schultz

    Denise Schultz

    Instructional Math Coach
    May 13, 2019 | 10:42 p.m.

    Hi Madhavi.  Thank you for sharing your video with us.  Your intervention materials use two of my favorite tools to explore fractions - cuisenaire rods and the number line so I was excited to see this.  I think your choice to pair the two lends itself to make connections between the concrete representation of Cuisenaire Rods, the visual representation of a number line and the abstract representation of a numerical expression when operating with fractions.  Did the 52 lessons move students through a gradual release of the CRA (Concrete Representational Abstract) approach or were all three models use in conjuction of one another throughout the program?

  • Icon for: Robin Schumacher

    Robin Schumacher

    Sr. Research Associate
    May 14, 2019 | 08:16 a.m.

    Thank you for your question on representations. We used Cuisenaire Rods and number lines iteratively throughout intervention to build understanding and then on an as needed basis. We included a "gradual release" in that students were asked to solved problems without representations; however, if needed we would bring them back to help students solve problems and evaluate the correctness of their answers. Our goal in using them was to help students understand the underlying concepts of fractions and fractions operations to support their problem solving. 

    Discussion is closed. Upvoting is no longer available

    Denise Schultz
  • Icon for: Beth Sappe

    Beth Sappe

    Director - STEM Mathematics
    May 14, 2019 | 02:34 p.m.

    Thanks for sharing the video. I appreciate that you are including the concrete manipulatives and making connections to the number line to unpack the fraction standards. What was the fraction screening measure that you used? When are students receiving the intervention, during pull outs in math class?

  • Icon for: Robin Schumacher

    Robin Schumacher

    Sr. Research Associate
    May 15, 2019 | 12:27 p.m.

    Hi Beth, we used a screener called Test of Understanding Fractions - 4th grade (TUF-4) that we created in house based off of released NAEP items and other items nominated and then vetted from mathematics educators. Since our focus was fifth grade students who struggle, we used this fourth grade measure, which is based on standards at 4th grade, as the screener. As for the second part of your question, tutoring was in groups of 5 and was pull out. Some schools had an intervention period and some schools scheduled us to come as part of their core math block. 

  • Icon for: Leanne Ketterlin-Geller

    Leanne Ketterlin-Geller

    Higher Ed Faculty
    May 16, 2019 | 07:03 p.m.

    I enjoyed your video and learning more about this research study. You mentioned that your sample included students performing between the 15-28th PR. Did your sample also include students with disabilities? Also, what instructional conditions did your students in the control group receive?

  • Icon for: Jessica Hunt

    Jessica Hunt

    May 17, 2019 | 05:01 p.m.

    Hi Robin!

    Thanks for this video detailing your study.  I appreciated the details around your work and the different instructional components outlined in your video.

    I noticed that you also included opportunities for problem solving as a part of your program. I'm wondering what those opportunities looked like in your program and if you could share a little more about that.  Thanks!


  • Icon for: Robin Schumacher

    Robin Schumacher

    Sr. Research Associate
    May 20, 2019 | 11:52 a.m.

    Hi Jessica, the word problems were included for the four operations with fractions after concepts had been explored using Cuisenaire Rods, semi-concrete pictures of Cuisenaire Rods, and number lines. The word problems were used to contextualize the operations and students were able to use the manipulative or draw number lines to aid in problem solving. 

  • Icon for: Rebecca Borowski

    Rebecca Borowski

    Graduate Student
    May 17, 2019 | 11:08 p.m.

    Hi all! Thanks for sharing this video - I enjoyed hearing about the intervention and am eager to read more about your work! 

    In answer to your first question - Yes, the video made me eager to learn more about the instruction in the curriculum. Specifically, I am interested in learning more about the use of number lines. The materials in the video made it seem like the number line work was focused on the positions/locations of the fractions on the number lines (i.e. 1/5 is closer to 0 and 10/12 is closer to 1). I'm curious whether you had students considering the fractions in terms of length on the number lines? (i.e. 1/2 of a unit is longer than 1/4 of a unit) Did students ever lay the Cusineaire Rods on top of the number lines, to integrate the 2 representations? 

  • Icon for: Robin Schumacher

    Robin Schumacher

    Sr. Research Associate
    May 20, 2019 | 11:53 a.m.

    Hi Rebecca, Yes we did emphasis the measurement interpretation of fractions, i.e., the distance from zero, when representing magnitude. 

  • Icon for: Madhavi Jayanthi

    Madhavi Jayanthi

    Lead Presenter
    Director of Research
    May 18, 2019 | 01:26 a.m.

    Hello Leanne,

    Sample included students with special needs such as attention deficit disorder; none had a specific learning disability in mathematics. Majority of the students in the control condition participated in whatever core academic instruction was being provided. Some control students received structured mathematics intervention or reading intervention.


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