# Program Review – JUMP Math

The JUMP (Junior Undiscovered Math Prodigies) Math program was developed by John Mighton, who lives in Toronto, Ontario. John create the JUMP Math with belief in mind that any student, despite whether they are gifted, average or have a learning disability, has the potential to excel in mathematics. The underlying philosophy of the program is that by breaking down math concepts into their smallest components and combining them with activities to build mathematical confidence, the differences in students’ abilities will be minimized and all students can be successful in math.

There are programs available from grades 1 through 8 and provide workbooks and teacher resources that are to be used every day in the classroom for the full year. They are available for purchase on www.jumpmath.org.

**Strengths**

The JUMP Math program prides itself on being an Ontario curriculum-based resource. JUMP Math covers the full curriculum for both Ontario and Western Canada through student workbooks, teacher’s guides, and a range of support materials. Despite satisfying the standards of multiple curriculums, it still covers the requirement outlined in the Ontario document.

There are many ways in which the JUMP Math program aligns with the principles underlying the Ontario Mathematics Curriculum, as outlined in the curriculum document. Firstly, the curriculum states that “students learn mathematics most effectively when they are given opportunities to investigate ideas and concepts through problem solving and are then guided carefully into an understanding of the mathematical principles involved” (p. 4). In a typical JUMP Math lesson, the teacher works with the whole class to lead students through a process of “guided discovery” while allowing them to adapt the lessons to their own level of understanding. These whole class lessons allow students to experience discovering knowledge about the concept together, as a collective rather than in an individual, competitive nature. The program’s method of “guided discovery” is very different from rote learning in that students are expected to take the steps themselves with the teacher as a guide rather than a lecturer.

Secondly, the Ontario Mathematics Curriculum states that the transition from elementary school mathematics to secondary school mathematics is very important for students’ development of confidence and competence. This concept of confidence in mathematics is pivotal for the JUMP program. The program starts with a 2-week long confidence building exercise that has demonstrably changed children’s perceptions of their abilities. In connection with JUMP’s approach to whole class lessons, the program promotes the idea that by following the program, students will feel more confident in their math abilities and thus will succeed in the subject

Lastly, the program aligns with the views of the curriculum in recognizing the diversity that exists among students who study mathematics. It provides teachers with resources to differentiate the learning of students. These resources include additional questions and multi-modal approaches to solving math problems, among others.

To further the conversation on differentiation, the Ontario Mathematics Curriculum explains that it is important to make valuable accommodations or modified expectations for students of varying exceptionalities. The JUMP Math program aides with differentiation by providing multiple representations of the same or similar concept help to reach a broader number of students. On the JUMP Math worksheets, concepts and skills are introduced one step at a time, with lots of opportunities for practice. The teacher’s guide suggests that struggling students can complete all of the questions on a worksheet while students who excel can skip some questions and do some extra work or bonus questions. The teachers’ guide even provides teachers with a 7-step process of making appropriate bonus questions for advanced students.

Lastly, the JUMP Program takes into account the fact that children are easily overwhelmed by too much new information. Students also require practice to consolidate the skills and concepts being taught and they benefit from immediate assessment and careful scaffolding of ideas. The program is mainly structured around the scaffolding model, in which students practice inquiry in manageable steps, mastering a concept before moving on. This proves to help immensely with student confidence and concept consolidation.

**Weaknesses**

While the JUMP Math program describes itself as a complete resource for the classroom mathematics period, there proves to be a number of weaknesses in the program. First, let’s outline some of the generic weaknesses of the program. JUMP Math only offers programs for grades 1 through 8, which may prove to have a negative effect on students once they transition into the high school grades. If students get used to this singular framework of learning math, then they may struggle with the new structure come high school, especially if their classroom adopts a critical thinking and discovery-based method rather than scaffolding. Additionally, the program seeks to minimize the differences in students’ ability by having them work on the same material at the same pace. By using materials and methods that minimize differences, teachers can cover more of the curriculum and can narrow or close the wide gap in student performance that exists in most classrooms. While this may prove to make it easier for the teacher, it might not translate into the students’ learning. The scores of the low-level students may rise with this approach; however, it could be at the sacrifice of lowering the high achiever’s scores.

Arguably one of the largest downfalls of the JUMP Math program is that many of the process expectations are not fulfilled. *Problem solving* requires students to develop problem solving strategies. Even though the program has a “guided discovery” approach, they still provide students with the way to solve each problem. Pedagogy teaches us that students’ best learn mathematic concepts through practical exploration and critical thinking. The heavy reliance on workbook material goes against this research. *Reasoning and proving* requires students to develop reasoning skills and use them in during investigation. There are very few reflection questions present in the student workbook, thus emphasising that the focus is on mastering the skill rather than comprehending the concept.

Through the scaffolding model approach to learning mathematics, the JUMP Math questions are very direct to one aspect of a concept and the workbook provides spaces for students to write their answers. These spaces only allow students to complete the question using the method introduced at the top of the page (Appendix A). As such, students are unable to fulfill the *selecting tools and computational strategies* expectation. The workbook is organized into sections by curriculum strand and is to be completed in a linear fashion, completing pages in order within those strands. Students who struggle in one area must experience that strand, and only that strand, until it is completed. Additionally, this does achieve the *connecting* process expectation, in that cross-strand integration of knowledge is not achievable.

The *communication* process expectation is very much concentrated on the students’ ability to write their mathematical thinking, rather than orally or visually present their understanding. Even when students are asked to communicate work visually, the students are only given one way to do so (i.e. Draw a number line to communicate…). This does not allow students the ability to practice or perform the skill of demonstrating understanding by freeing communicating in whichever mode they chose.

Many aspects of the specific expectations in the Ontario Mathematics Curriculum are not fully achieved. Specific expectations that require the use of a “*variety of mental strategies”* are not fulfilled in the scaffolding method. In the JUMP Math program, students are expected to master one concept at a time using the strategy provided to them in their workbook. This also means that expectations beginning with “*select and justify*” or “*create and analyse*” will also not be achieved, since students can only use the strategy expected of them for that given question.

Students also fail to achieve specific expectations such as “*through investigation using concrete materials, drawings*…” and “*determine through investigation using a variety of tools*”. While the workbook sometimes asks students to draw when answering a question, the specific image to be drawn and method of drawing it is outlined for the students (Appendix B). Also, at the end of the day, students are only using one concrete tool: their workbook.

**Conclusion**

Admittedly, the JUMP Math program is enticing, especially for a newly hired teacher. The program contains a complete, year-long resource that allows the teacher to facilitate learning without the planning. It comes with a full workbook for each student, a detailed teacher manual, and SMART Board material that corresponds with each lesson.

Although the program prides itself on covering the entire Ontario Mathematics curriculum, the pedagogy in teaching methods and critical thinking prove to be ill-aligned. There will be a select few students that truly enjoy having a workbook as a focus for the majority of the lesson; however, there will be more students that would prefer to *discover* the concept through hands-on problem solving rather than pencil to paper.

The fact that the specific expectations are the focus on the program is practically irrelevant when looking at how many process evaluations are not fulfilled. Communication, reflection, and making connections are extremely important to the student’s learning, especially when working with a subject as complex at math. Critical thinking is a powerful way to promote student’s ability to use many different pieces of information to come to unique solutions to problems. However, the JUMP Math program introduces students to one concept at a time, instructing them how to achieve the required result before moving on to the next component. This scaffolding method, while important for understanding the essence of the concept, does not allow students to think critically about why that method works or how it can be used in another way.

With all this being said, I believe the program has merit in introducing students to the specific skills needed to understand a larger concept. Therefore, it would be a beneficial program to have as a supplementary material to activities, problems, and math games. If these two concepts were used in conjunction with one another, it would allow students to learn math in a variety of ways while also taking them through the learning process of scaffolding skills and utilizing them in practical situations. Based on the information outlined in the Ontario Mathematics curriculum, I do not believe that JUMP Math should be used as the only resource.

**Works Cited**

Mighton, J., Sabourin, S., & Klebanov, A. (2009). *JUMP Math 6.1* (2009 ed.). Toronto: JUMP Math.

*The Ontario curriculum, Mathematics, Grades 1-8* (Rev. ed.). (2005). Toronto: Ontario, Ministry of Education.

**Appendix A**

Dr A W PasternakonVery interesting Mr Spencer- that considered critique of JUMP Math. Am thinking of using JUMP for early years to help prevent the attainment gap growing- indeed to help reduce it. By attainment gap I mean the difference of achievements any cohort of children will have when they first arrive at school. Sadly, I am not aware of any primary/elementary schools nor settings in which such disparity does anything but increase as children move through their school years.

Your views would be appreciated on how effective the use of JUMP methods and materials might be.