Daniel Ansari Tweeted the short video above so I took a look and I would encourage you to do the same. I was vaguely aware of JUMP Math. There has been much discussion of Canada’s declining maths performance in international studies such as PISA and TIMSS and I have heard JUMP Math mentioned as a possible solution.
I was struck by the claim in the video that JUMP Math uses ‘guided discovery’ learning. If you visit the JUMP Math website, this claim is repeated and a link is provided to the Alfieri’s et. al. paper that relates to this topic. In fact, this paper compares a range of conditions it labels ‘enhanced discovery’ with a range of other things that could include working from textbooks. One of the enhanced discovery conditions is ‘guided discovery’ but the authors don’t really explain what this is (the others are ‘generation’ and ‘elicited explanation’). The best definition that they offer is that guided discovery conditions, “involved either some form of instructional guidance (i.e., scaffolding) or regular feedback to assist the learner at each stage of the learning tasks.” And anyone who has followed this area will know how diffuse the concept of ‘scaffolding’ is.
This is messy. One common response to the famous Kirschner, Sweller, Clark (2006) paper on ‘minimal guidance’ is for constructivists to claim that their preferred methods contain loads of guidance and so it cannot be described as ‘minimal’ – Kirschner, Sweller and Clark have misunderstood! However, as Alfieri et. al. point out, “although guidance has been an important component of instruction on both sides of the debate concerning constructivist instruction, there remains a remarkable number of discovery-based instructional tasks that are largely unassisted.”
In contrast, explicit instruction is reasonably well-defined. Rosenshine lists a number of key features but probably the most important ones are that new material is presented by the teacher using lots of examples before students are asked to practise, and that this new content is presented in small chunks. Explicit instruction does not start by considering a complex performance or product; it builds learning in small, incremental, sequenced steps.
There are some samples of JUMP Math materials available online. It is hard to tell a great deal about sequencing from these discrete samples although you can tell that that prior knowledge is considered critical because the teachers’ guide lists the knowledge that is required. It also reads a little like a script; not quite to the same level as an Engelmann Direct Instruction program such as Expressive Writing but it’s not too far away. There are details of the examples to use and questions to ask. I’m not alone in recognising something familiar here. A modification of JUMP Math aimed at College students is described by the authors of a randomised field trial as, “an explicit instruction method.”
You have to ask: exactly what are the students discovering? It seems as if they are discovering the concepts that the teachers explain to them.
It will be interesting to see how JUMP Math develops over the next few years. Unlike many programs, the ‘research’ section of the website is fruitful and contains evidence from randomised controlled trials. The fact that they are using an explicit instruction method leads me to think that this evidence base is likely to grow. I will be paying attention.
Filling the pail 
Reblogged this on The Echo Chamber.
Even though JUMP is a proven success w/students and teachers, many school districts consider it to be a cult. Some districts have gone as far as to ban JUMP in their schools, and some teachers have found themselves transferred out of their Districts for using it in the classroom.
Does JUMP work? Hundreds of parents and teachers I have spoken to, indicates a resounding “YES!”. A workshop I attende where John Mighton led the discussion, electrified the room. JUMP isn’t a cult; rather it’s effect on teachers and students is unblievable. The “guided discovery” aspect should not be confused w/inquiry only. JUMP’s principles always insist that teacher led instruction be front and centre of each lesson, and that kids master the basic steps before advancing to the next level. For those kids at different levels in the classroom, JUMP has harder and/or easier lessons tailor made to suit ALL kids.
I was fortunate to have Liz Barrett, First Nations coordinator and JUMP manager, present at our meeting in May. It was one of the most inspiring presentations I’ve heard.
I encourage all teachers and parents to try this valued resource. You’ll be glad you did.
Re: “The guided discovery aspect should not be confused with inquiry only.” What about the concept of “guided inquiry”, Tara, rather than ” inquiry only”. I gather you are referring to concerns with and evidence supporting the ineffectiveness of minimally guided or unguided inquiry and discovery, concerns I share, and evidence I acknowledge that matches my experiences. However, the term “guided inquiry” can be and is used to mean the same as guided discovery- the activities in both cases being student centred but teacher led, as Mighton describes and explains in the article posted by Ben Wilbrick later in this thread. It seems as though some people refuse to acknowledge that the terms “inquiry” and ” discovery” can be used in descriptions of effective teaching methods that help students to build and extend their understanding of math concepts etc, and develop proficiency with skills.
If you look at the books the founder John Mighton wrote several years ago you won’t see much about discovery. In fact you will see the opposite:
From The Myth of Abiltiy
“Some educators believe that teachers can actually arrest or delay the intellectual development of their students by teaching them how to perform an operation (such as adding fractions) before they have learned the concepts underlying the operation. However, while it is true that children who understand mathematics show ultimately be able to explain how they found a solution to a problem or why a rule works, it does not follow that a child who initially learns an operation by rote has no hope of learning the concept later. I learned fractions by wrote and I think I can claim to understand fractions.
The idea that it is always harmful to teach rules before concepts is not supported by the actual practice of mathematics. John von Neumann, one of the great mathematicians of the 20th century, said that understanding mathematics is generally a matter of getting used to things.” p 61
This was published in 2003.
Mighton holds a PhD in mathematics from the University of Toronto. He knows what he is talking about when it comes to how mathematicians think about math.
His basic advice in teaching math is whenever a student doesn’t get something break it into smaller steps and have them master the each step before moving on. The Jump material is also prescriptive enough that anyone with basic math can use it to teach it (it runs to grade 8 only). The original Jump material was written as books for parents to help kids with homework.
Except as an attempt to fit the ideas popular with school administrators it is hard to understand all the language about guided discovery.
In Canada I suspect if Ministries and boards adopted the Jump math approach all those calling for changes would just say thank you and stop complaining.
But you won’t find Jump math mentioned on the Ontario Ministry of Education website. It is pretty damming that a charitable organization can win awards and world wide recognition, publish research on their approach and yet there is not even the suggestion from the Ministry of education based in the same city that it exists.
And this from a ministry that puts out these offerings as the best research available for educators:
Click to access WW_SpaceThinkMath.pdf
Click to access WW_trigonometryGr3.pdf
These are parodies of what research summaries should look like – sprayed with references to give the appearance of evidence supported conclusions but never describing the confidence level in the conclusions or costs and tradeoffs involved in the approach suggested verses the best alternatives.
This one
Click to access WW_trigonometryGr3.pdf
Is all about how children may be more capable in math than some people think and this may be holding back engagement and enjoyment of math.
No mention of Mighton and his books The myth of ability and The End of Ignorance despite other 15 references. Published in 2012 what would motivate the authors to exclude mention of Mighton?
But it does have the dodgy claim that you can have parallel lines on a sphere that meet. No explanation is given for in what way these lines are parallel or even how to define a line verses a curve on a sphere.
It is the antithesis of Mighton’s approach which is generally to take something considered challenging to learn – such as adding fractions and have students master it and get a thrill our of mastering something without worrying about some neat idea. If you are going to publish on ways to excite and accelerate the understanding of math how would get away with avoiding talking about an alternative approach to doing this.
Greg,
It has been an interesting post. I’m a spanish teacher using JUMP Math and one thing that has surprised me is that uses the main principles of the explicit instruction. This makes of JUMP Math one of the few math methods with this vision. The method can also be combined and complemented with cooperative learning activities, metacognition work…
Do you have any references about the Singapore Math method? Is it similar to JUMP Math? Which differences there are between both of them? In my context (Spain) I think that this two are of the few math methods with evidence.
Thank you and sorry for my written english (I’m not an expert)
Thanks for your comment. It is interesting that you are using this approach in Spain. I don’t know a huge amount about Singapore maths other than what I have read in blogs etc. I probably need to do some research.
I purchased a JUMP workbook for a son several years ago. It was something extra because I never liked his math programs in elementary/middle school years (too many poorly worded word problems, TONS of estimating and a lot of jumping around). I really liked what I saw of JUMP. I really believe in the “breaking it down” approach.
My son is now a 10th grader in a charter school. He has no math teacher. He uses ALEKS, an online program. Now, I am generally not one to think that computers can do a better job than teachers–both my husband and I are teachers! However, by the time he got to 8th grade we’d had it with all of the constructivist, common core teaching. Everything was–throw the kids into a group, give them a HUGE, long term project and let them figure it out–with pretty much ZERO guidance. With this as the only other option, an on-line program with no teacher starts to look pretty good.
Our experience with ALEKS has been quite good. My son does not love math and while he isn’t horrible at it he needed TONS more repetition and practice with concepts than the regular classroom allowed for (the generally taught 3-5 ways of how to solve a problem simultaneously and then after 1-2 weeks tested them on ALL the ways presented, handed him a C or D and moved on to completely new concepts). So, ALEKS is pretty straight forward in it’s presentation, allows some choice of which topic to work on but only those that the student is ready for are options. Every 20-25 sections there is an assessment. SOmetimes he does very well. Other times he drops back and is forced to repeat sections (he needed extra repetition). We love it because even it guarantees eventual success. Sometimes he’s able to meet with a tutor during the school day and often I help him if he’s stuck. I’d be curious if you’ve heard of this program and what your thought are on it. From my experience I would say that it is very incremental just like JUMP.
I’ve not heard of ALEKS. I’ll look it up.
John Mighton (February 2014). JUMP Math: Multiplying Potential. Notices of the AMS, volume 61, #2, 144-147.
Click to access rnoti-p144.pdf
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