In a variety of studies, including two randomized controlled trials, JUMP Math has produced significant improvements in students’ achievement and attitudes in math. For details, see Research that Directly Supports JUMP Math below.

The principles of instruction on which JUMP Math lessons are based are also supported by a wide range of research in cognitive science. For a summary of this research, see Research Supporting the Principles of Instruction used in JUMP Math.

The results of JUMP Math have been featured in various scientific journals, such as Scientific American Mind, and at scientific conferences, such as the Aspen Brain Forum and the conference on Brain Development and Learning where Dr. Mighton gave keynote addresses. Many distinguished cognitive scientists and educational researchers support JUMP or are working with JUMP as research partners. JUMP Math is listed on the Evidence for ESSA website.

## Research that directly supports JUMP Math

- Two-year randomized controlled trial
- Six-month randomized controlled trial
- Autonomous University of Barcelona
- Lambeth
- JUMP Book Fund Schools
- Case Studies
- JUMP Math-Brock University Pilot Study
- Studies on Attitude
- Vancouver School Board (2007)
- Effects of the JUMP Math Program on Elementary Students’ Confidence (OISE, 2004)
- The Impact of JUMP on Studen Math Confidence (2004)
- Research that supports JUMP Math methods of instruction
- Supporting ResearchBarriers to paying attention and being engaged in math lessons

## Two-year randomized controlled trial

In 2013 to 2015, JUMP Math participated in a large-scale randomized controlled trial that was funded by the US Department of Education. The results were published in the scientific journal PLOS ONE in 2019. Here are some highlights:

The researchers used two main measures, Broad Math (which measures achievement in fluency, computation and applied problem solving) and Problem Solving Processes (which measures achievement in the types of word problems that appear on state and provincial tests).

The researchers point out (based on a review of the literature) that an effect size of .3 is rare in intervention studies and that an effect size of .5 is extremely large. We have included the effect sizes below.

In the grade 2/3 cohort, the researchers were able to identify teachers who used either the JUMP Math program or the incumbent math program with high fidelity. In year 1, students in the control group made significantly more progress than students in the JUMP group on Broad Math (ES .24), but both groups made more progress than expected relative to the norm. However, in the second year, students in JUMP classes made significantly more progress in Broad Math (ES .26), Applied Problems (ES .12), and Problem Solving Processes (with a very large effect size of .54).

In the grade 5/6 cohort, researchers were not able to isolate high fidelity groups, as some of the teachers in the control group used JUMP methods and materials in grade 6. However, in year 2 of the study, in the general population, JUMP students made significantly more progress in Broad Math than students in the control group (ES .22). In both years, JUMP students made more progress in Broad Math than expected relative to the norm.

JUMP achieved these results in spite of some disadvantages. For example, the teachers in the JUMP Math group only had two days of training (and no observations or coaching). As well, the JUMP teachers didn't have a chance to get better at implementing the program over time, as almost all of the teachers in the second year of the study were new to JUMP. Link to the paper.

## Six-month randomized controlled trial

JUMP Math participated in a 6 month randomized controlled trial in 30 classrooms. The students were tested (pre and post) on Fluency, Computation and Allied Concepts. JUMP students made significantly more progress relative to the norm in Fluency and Computation, while control group students only made the expected rate of progress on these measures. In Applied Concepts, control group students made significantly less progress than the norm, while JUMP students made the expected rate of progress. Link to paper

## Autonomous University of Barcelona

The Autonomous University of Barcelona conducted a one-year study of JUMP Math with 1000 grade 5 students. Before JUMP, the average score of the students on a standardized test of mathematical knowledge was 3.1 points out of ten. After a year of JUMP, the average score was 5.2 points. 85% of the students improved their scores on the test. Teachers and parents rated the improvement in students' attitudes about math to be medium to high. Many teachers were impressed by the progress their students made. For example, one teacher said: "I have a girl with very serious emotional problems who was a 1 and was very unmotivated. Now she is a 4. A 4 was unthinkable, it was unthinkable." Link to paper

## Lambeth

Between 2006 and 2010, JUMP participated in a large pilot in London England, in the borough of Lambeth. Each year, approximately 500 behavioral and special education students used JUMP as their core math program. Roughly 20 percent of the students in the pilot were considered to be at grade level when they started JUMP. Each year approximately 60% of these students passed the national exams in math. Teachers reported significant improvements in student behaviour and attitudes towards math. The graph below shows the results for 2008. The improvements in each year were similar:

Here are more details about the pilot:

### The Impact of JUMP Math in England - Lambeth (2009)

JUMP Math has worked for four years with the Borough of Lambeth, an inner-city area of London which is the third neediest borough in England. Several independent studies of JUMP Math have been conducted by the Lambeth school board. The results are contained in reports written by Nikki Aduba, Mathematics Consultant.

The results presented in the 2009 report from Lambeth are for two groups of students who wrote the Year-6 exams in 2009. One group of 353 students used JUMP Math for two years, beginning in Year-5, and another group of 110 students used it for one year, beginning at the start of Year-6.

Of the first group of 353 students, only 12% were performing at or above grade level when they began using JUMP Math at the start of Year-5. By end of Year-6, after two years of instruction using the JUMP Math materials and approach, fully 60% of this cohort were at or above grade level (a five-fold increase).

Of the second group of 110 students, 28% were performing at or above grade level when introduced to JUMP Math, at the beginning of Year-6. By the end of Year-6, after one year of instruction using the JUMP Math materials and approach, 62% of this cohort were at or above grade level.

The greater rate of improvement among children who used JUMP Math for two years vs. one, appears to bear out teachers’ qualitative assessments that progress with JUMP Math accelerates over time.

### Lambeth (2007)

In 2007, Lambeth experienced a rise in its national test scores in mathematics by 7 percentage points, moving from close to the bottom to within two points of the national average. Based on JUMP Math's success in Lambeth, the program was recognized by the UK Department for Children, Schools and Families in the report "What Works for Children with Mathematical Difficulties?". Lambeth was awarded a grant by the London Challenge to make JUMP Math available to more students in Lambeth and other boroughs.

The 2007 report, "JUMP in Lambeth 2007: Evaluation and Impact on the KS2 National Tests", contains the following history of the JUMP Math pilots in Lambeth:

- "In the 2006 summer term, 24 Lambeth primary schools participated in a pilot programme to evaluate the JUMP mathematics methods and materials... Following on from the success of the pilot, work continued and developed in 40 (out of 59) Lambeth primary schools... In all schools teachers where asked to target those children who were not expected to achieve level 4 (ie. meet age-related expectations) on the national tests at the end of Y6."
- Four hundred fifty-four students, 90% of whom were at least 2 years below age-related expectations at the start of the school year, received 4 to 10 months of JUMP instruction during the 2006-07 school year. The national test results at the end of the year were particularly strong among children who were 2 years below age-related expectations:
- "Of the 154 children who were at Level 3c pre-JUMP Math (that is, 2 years below age-related expectations), 107 children (69%) were at or close to age-related expectations one school year later." (60% passed the exams and 9% came within a few marks.) Overall, 33% of the students achieved level 4 on the exams (met age-related expectations), even though 60% were more than 2 years below age-related expectations at the start of the pilot.
- The report also notes, "Half of the JUMP Math children (225, 50%) made at least two sub-levels of progress through the year. This was an acceleration on their progress in earlier years (otherwise they would not have been so far below age-related expectations at the end of Year 5)."
- "Improvements in confidence and attitude of all children participating in the program are almost universally reported…” and the "effective use of the JUMP Math materials in accordance with the programme's principles and methodology has the potential to support teachers to raise the quality of their teaching (and therefore children's learning) from satisfactory or good to outstanding. There is a growing body of evidence that this is happening…”

### Lambeth (2006)

In the summer term of 2006, prior to the larger implementation reported above, 24 schools in Lambeth, England, used the JUMP Math program with children who were at least 2 years below age-related expectations. Based on the success of this pilot, the program was then expanded to 40 schools (as reported above).

The attached report, "JUMP Mathematics: Lambeth Pilot Programme, Summer 2006," contains the results of interviews with teachers and data on pre- and post-test scores (samples questions from the national exams were given to the students before and after the pilot).

The report notes:

- "The response to the JUMP pilot has been overwhelmingly positive, from the interest shown at the time that schools were first invited to participate, to the enthusiasm of the final review meeting on 18 July. Without exception all participating teachers want further involvement with JUMP..."
- "All teachers reported a significant improvement in attitude in the vast majority of pupils participating in the pilot. The children became far more confident and were eager to speak out and actively participate during mathematics lessons. Teachers also commented on increased self-esteem of pupils who had hitherto (for years in some cases) seen themselves as failures in the subject. Behaviour also improved; children who had been disruptive during lessons were engaged, focused and enthusiastic during the JUMP sessions."

Even though the summer pilot lasted only two months, "A significant number of children improved their test scores enough to move one, or even two sub-levels... Many teachers felt that the improvements in children's understanding was considerably greater than their test scores might indicate."

### The Borough of Lambeth, UK raises its year-6 pass rate by 10% (versus 2% for England as a whole), since introducing JUMP in 2007

The Borough of Lambeth school authority tracked two groups of students who wrote the year-6 national exams in 2009, one of which used JUMP for two years and the other of which used JUMP Math for one year. Only 12% of the first group of 353 struggling students were at or above grade level at the beginning of year-5 and many were several grades behind; yet 60% of this group passed the national exams at the end of year-6 (a 5-fold rise in pass rates). A second group of 150 students used JUMP Math for one year. Only 28% of these students were at or above grade level at the start of year-6, many being several grades behind, yet 62% passed the year-6 exam. The Borough's year-6 pass rate rose from 6% below the national average in 2007 to 2% above in 2010.

In 1998, the percentage of children achieving the expected level in mathematics in The Borough of Lambeth trailed the national average by 9% (49% vs 58%). By 2007, the year that JUMP Math was introduced in Lambeth, Lambeth's pass rate had risen to 71%, but remained 6% below the national average. Three years later, Lambeth's year-6 mathematics achievement exceeds the national average by 2%.

This progress is a result of many factors -- Lambeth teachers and children have worked hard with a range of supportive resources -- however, Nikki Aduba, the former Mathematics Consultant for the Borough of Lambeth, stated that "JUMP Math has made a hugely significant contribution to the success of children who are now working through secondary school as competent and confident mathematicians".

To date, the gains in Lambeth have been achieved using JUMP primarily to assist those children who are having the most difficultly with the existing math programs; however results obtained in Canada suggest that it is equally effective for all students, including those considered to be "gifted" in math.

## JUMP Book Fund Schools

In 2018, for the seventh year in a row, the growth in math achievement in JUMP Math students grew at a minimum of 2.4 times the rate of the WRAT-4 norms. In the 2017-2018 school year, a total of 240 students in grades 4 to 7 completed the math computation subtest of the WRAT-4 in the fall and spring of the school year. Here are the highlights:

- On average, math achievement of students grew at 2.8 times the rate of the WRAT-4 standardization sample
- The number of students scoring ‘average’ or above increased from 50% in the fall to 69% in the spring
- The number of students scoring ‘above average’ or higher increased from 4% in the fall to 10% in the spring.

Download the full NBF 2017-2018 report

Download previous NBF Reports: 2016-2017 | 2015-2016 | 2014-2015 | 2013-2014 | 2012-2013 | 2011-2012

JUMP Math’s National Book Fund program awards free JUMP Math resources to classrooms across Canada. The National Book Fund was made possible by the generous support of lead funder TD Bank Group. More about the National Book Fund here.

## Case Studies

### Brooklyn

Between 2017 and 2019, four schools in Brooklyn implemented JUMP Math with fidelity across all grades and one school implemented the program in two grades. In 2019, two of the schools achieved striking gains on the New York state tests. In one school, the number of students scoring proficient increased by 23 percentage points (doubling the number of students who passed the exams) and, in another, the number of students scoring proficient increased by 25 percentage points (tripling the number of students who passed). By way of comparison, in a sample of 100 NY City schools, only 4 had gains over 20 percentage points and all were less than 25 points. As well, between 2017 and 2019 all of the JUMP schools achieved significant gains in all grades: in more than half of the grades the number of students achieving proficiency roughly doubled (with even more dramatic gains in some grades). The schools also significantly increased the number of students achieving level 4 and reduced the number of students at level 1. Use Mike’s graphs here:

### Manhattan

In 2014 the Manhattan Charter School achieved the greatest gains on the New York state tests in math of all schools in the city (a 32 percentage point gain according to Chalk Beat). In 2018, two master teachers using JUMP in grade 4 at the school increased the number of students scoring level 3 and 4 from 40% to 81%. 56% of the students scored at the highest level (level 4). By way of comparison, only 18% of grade 4 students in a school in the same building (with the same demographic) scored at level 3 or 4 (with only 3% at level 4). One of the teachers wrote a blog for Achieve the Core describing her students' attitudes towards math:

What I saw in those scores wasn’t even the full picture. Something special was happening in my classroom. Each day, my students could not wait to begin math. Even my lowest-achieving students were jumping out of their seats to answer questions. I will never forget one student in particular who cried at the beginning of the school year because math was so difficult for her. She quickly got on board with JUMP Math and received a four (the highest rating) on the New York State Test that same year. Thinking of her achievement still brings tears to my eyes.

(NOTE: The teachers have since moved to new schools.)

### Toronto

During her first year using JUMP Math, a Toronto teacher lifted her class average ranking from the 66th percentile on the grade 5 TOMA (Test of Mathematical Ability) test to 92nd percentile on the grade 6 test, in September of the following year. Her next class improved its average ranking from the 54th to 98th percentiles. The teacher reported that she followed the JUMP Math lesson plans more closely with her second class. In both cases, the lowest post-JUMP ranking equaled or exceeded the highest pre-JUMP ranking. In addition, all but one child in each class wrote the Mathematica Centrum Pythagoras test and 14 of 17 achieved distinction. (The Mathematica Centrum Pythagoras math contest emphasizes problem solving and is written by approximately 5% of Canadian grade 6 students - in general, Canada's "top' math students).

## JUMP Math-Brock University Pilot Study

This study was a collaborative effort between JUMP, the Institute for Enterprise Education (IEE), and the Brock Enterprise Education Program (B.Ed. program). The timeline of the study was February 21- March 11, 2005. 160 students from grades 3-6 participated in the study.

A pre-test was administered to the students to get a baseline measure of their math ability prior to the implementation of the JUMP Math approach. After the duration of the JUMP Math program, a version of the same test was administered to these students in order to measure any change.

The following is a selected summary of the results:

- Of 160 students who participated in this study, 0% of students passed the pre-test; after the implementation of the JUMP Math program, 100% of students passed the post test (average math post-test scores by classroom ranging from 77%-92%).
- Of 160 students, the average test score improvement was 74%.

After the implementation of the JUMP math program, 100% of students showed an improvement in their post test scores (minimum improvement was 22%, maximum improvement was 100%). Download full report

## Studies on Attitude

Carol Dweck, the psychologist who demonstrated the importance of positive mindsets in math and other subjects, has said that JUMP lessons incorporate "growth mindset principles." A video of Dweck talking about JUMP is posted on the home page of jumpmath.org. A number of studies of JUMP suggest that JUMP has a positive effect on students’ attitudes about math. Learn more here

## Vancouver School Board (2007)

Lavana Heel, a consultant with Learning Services at the Vancouver school board, interviewed approximately one hundred teachers after they had attended JUMP Math training sessions in the board. She asked the teachers to talk about what had led them to participate in JUMP Math professional development, and what aspects of the JUMP Math program they thought would be helpful in their teaching. Lavana then conducted follow-up interviews with twelve of the teachers who used the program through the school year and who had attended regular study sessions sponsored by the board. These teachers were asked a number of questions about the effect of JUMP Math on children's conceptual understanding of math (the questions were based on the work of Reuven Feuerstein).

The report notes that the interviews "...revealed definite themes that are supported by the recommended interventions and propositions in brain research such as those supported by David Sousa (How the Brain Learns) or De Fina and Fifer (The Neuropsychology of Mathematics)."

The report found "an overwhelming agreement" among teachers "...that the infrastructure and process of JUMP Math develops in teachers a confidence, self efficacy and a sense that they can do math and even love it. Teachers have noted that not only the students but also teachers themselves are beginning to transfer the skill set and strategies to other content areas."

According to the report, teachers who used the program for a year felt that it "...unfolds students' thinking skills, promotes independent thinking and serves to create excitement and curiousity" (see conclusion of report). Teachers also felt the program helped students to explore mathematical ideas systematically, to determine relevant and irrelevant information in a problem, to develop "logical thinking," to organize their thinking before they respond to a task, to develop "a feeling of internalized competence" and to articulate what they had learned. Teachers also believed the program helped students develop greater confidence and a willingness to take risks, and fostered "a sense of connection or belonging to the larger group."

## Effects of the JUMP Program on Elementary Students’ Math Confidence (OISE, 2004)

Based on a graduate research study conducted by Kaitlin Hughes at the Ontario Institute for Studies in Education (OISE) at the University of Toronto, this study examines JUMP Math and its effect on students’ math confidence. A pre- and post-survey were administered to 120 students in six different classrooms at three different schools. Participants ranged from grades 3 and 4 students who had never worked with JUMP Math curriculum before.

Analysis of quantitative and qualitative data shows that there is “a very significant relationship between students’ math confidence and the JUMP program”. Analysis reveals that “students both enjoy the program and feel more confident about their math education after receiving the program”.

- Research shows that with the pervasiveness of math anxiety and negative attitudes towards math in students, there is a need for math program to encourage confidence-building.
- Statistical analysis of math confidence scores reflects an overall growth and statistically significant increase in math confidence from pre-JUMP program implementation to post-JUMP program implementation, with the most growth occurring in males.
- Of those students who participated in this study, most felt confident about their math work after having completed the JUMP program. JUMP Math students said they were successful in doing mathematics, they were not worried about doing math, and they felt confident about their skill level. 57.4% of respondents to the post-survey said they were good at math. 61.7% of respondents to the post-survey said they don’t worry about doing math in class.
- Of the 74 students out of 116 who identified a difference between JUMP math and regular math curricula, 88% commented that they favoured JUMP to regular math or like both programs. Students were able to notice a change in their math program and most students responded positively to the change.

## The Impact of JUMP on Student Math Confidence (2004)

This study examined 14 classrooms in 4 elementary schools in Toronto, Ontario over a four week period. A survey was designed by JUMP Math in consultation with academics from the Ontario Institute for Studies in Education (OISE/University of Toronto). The survey was administered by JUMP staff at the conclusion of the one-month study with the help of 10 interns from OISE.

- 100% of participating teachers said that students showed an improvement in student confidence in subjects other than mathematics as a result of using the JUMP Math program.
- 100% of participating teachers said they would use JUMP inclass next year.
- 100% of participating teachers said that their weaker students were more enthusiastic about doing math as a result of the JUMP Math program.

## Research that supports the JUMP Math methods of instruction

JUMP lessons are based on a method of teaching called "structured inquiry." In JUMP Math lessons, students explore and discover mathematical concepts independently in manageable steps, while the teacher provides sufficient guidance, examples, feedback and scaffolding for all students to meet their full potential. JUMP Math is recommended by the Canadian Language and Literacy Research Network as a program that "offers educators... complete and balanced materials as well as training to help teachers reach all students".

- J. Bisanz et al. (2010) Foundations for Numeracy: An Evidence-based Toolkit for the Effective Mathematics Teacher. Canadian Child Care Federation and Canadian Language and Literacy Research Network, p. 44.

In 2011, L. Alfieri et al. conducted a meta analysis of 164 studies of discovery-based learning and concluded that "Unassisted discovery does not benefit learners, whereas feedback, worked examples, scaffolding and explicit instruction do." The authors recommend "enhanced discovery" (discovery with the instructional supports mentioned above) as the most effective approach to instruction in mathematics.

- Alfieri, L., et al. (2011) Does Discovery Based Instruction Enhance Learning? Journal of Educational Psychology, Vol. 103, Issue 1, p 1-18.
- See also the references below for evidence that discovery needs to be balanced with rigorous guidance: Anderson (2000), Gobet (2005), Van Merrienboer (2005), Ross (2006), Kirshner (2006).

JUMP Math's extensive Teacher Resources are the core of the approach. The lesson plans in the guides cover the full curriculum and include ideas for contextualizing mathematical concepts, mini-assessments and questions for formative assessment, problems and challenges that allow students to investigate and develop concepts, mental math exercises to help students develop computational fluency and automatic recall of facts, extension questions for students who require additional challenges, and a variety of games and activities with concrete materials. The student Assessment & Practice books help teachers assess whether students understood the lesson and give students sufficient practice to consolidate skill and concepts.

JUMP Math lesson plans and materials allow teachers to differentiate instruction by providing extra practice, scaffolding, and continuous assessment for students who need it, and more advanced work for students who are ready for the next challenge. But while instruction is differentiated, the significant majority of students are expected to meet the same standards.

A growing body of evidence in education and cognitive science suggests that, with proper instruction, children can develop abilities in subjects for which they previously showed no real aptitude or gift. (See for instance, Ross, P. E. (2006) "The Expert Mind." Scientific American, July.) But research also shows that new abilities are more likely to emerge when a child's brain is attentive and engaged.

## Supporting Research:

- Posner, M., Rothbart, M. (2005) Influencing brain networks: implications for education, TRENDS in Cognitive Science, v.9, no. 3
- Gathercole, S. E., Alloway, T. P., Kirkwood, H. J., Elliott, J. G., Holmes, J., & Hilton, K. A. (2008). Attentional and executive function behaviours in children with poor working memory. Learning and Individual Differences, 18(2), 214-223.
- Schwartz, J., Bregley, S. (2002) The Mind and the Brain. NY, Regan Books.

In designing the JUMP Math resources, we asked:

### What barriers prevent students from paying attention and being engaged in math lessons?

*Click on the posters below to read research that supports common barriers and our strategies for teachers.*

- Barrier 1: Students who are anxious or who lack a sense of self efficacy have trouble focusing and staying on task.
- Barrier 2: Students who feel inferior are less likely to be engaged in their lessons. In early primary school, children start to believe some children are superior or "smarter" in math.
- Barrier 3: Students who believe that success depends on innate ability do poorly compared to those who believe that success depends on effort.
- Barrier 4: Research has shown that students need extensive practice to master new concepts and skills, but they aren't always motivated to practice.
- Barrier 5: The brain is easily overwhelmed by too much new information; math problems that are too complex or overly contextualized or texts that have too many new ideas on a page can discourage and confuse students.
- Barrier 6: Weak readers and ESL students can be overwhelmed by too much text, making their language challenges a barrier to achievement in math.
- Barrier 7: It is important to teach mathematics using models, but sometimes concrete materials can be distracting or confusing: students don't necessarily learn efficiently from using manipulatives in unstructured lessons.
- Barrier 8: Students who haven't mastered basic number facts and operations and committed them to long term memory must use short term memory to do so, leaving inadequate short term memory capacity for problem solving. Students who haven't mastered basic number facts also have trouble seeing patterns and making estimates and predictions.
- Barrier 9: Students often memorize rules or procedures without understanding. This may enable them to answer narrowly put questions, but without promoting true understanding: math doesn't always make sense to them.
- Barrier 10: To succeed in later grades, students must master the concepts and skills taught in the elementary curriculum. But many students never master these skills and concepts, even though the vast majority are capable of doing so.