It seems that one of the many catch-phrases and beliefs in education circles is “engagement”. The thinking is that if we can just get kids to engage in the material, then they would be interested enough to learn what needs to be learned. I’m a bit old-fashioned when it comes to education as many well-meaning, outspoken people have told me, but I continue to believe that if students know how to do things in math, they find it more enjoyable. If they are struggling because they haven’t mastered basic foundational skills and facts, then despite what experts say, they are pretty much not going to like math all that much.

So it wasn’t surprising to read the latest article about some enterprising people (from U of Arizona and U of Delaware) with degrees in math education and a $1.3 million grant from the National Science Foundation who believe that if mathematics is proven to be “interesting and useful” to students, that’s one key to engagement. Their grant would explore what’s working to motivate students to learn math, recording reactions on a real-time basis.

**“This ASU-UD team is the first to research moment-to-moment experiences of high school students studying mathematics over time as part of their three-year, $1.3 million National Science Foundation-funded study, “Secondary Mathematics, in-the-moment, Longitudinal Engagement Study.”**

**” ‘We recognized a lack of research that could address, methodologically, how to investigate students’ experiences in the moment to understand the nature of their engagement with mathematics in a way that could reveal more general trends,’ Jansen said.**

**“By understanding these processes, they plan to help teachers to encourage more students to engage deeply, work hard, persist and become more mathematically capable.”**

I’m hoping that such study will indicate deficits students may have (like basic foundational skills and facts) that may hinder their progress on even the most interesting of problems.

I found this statement to be rather intriguing by the way:

**“It is entirely likely that there are many good ways to teach,” Middleton says, “but that some of those ways may be optimally effective in limited contexts.”**

Just a guess, and I know I’m sticking my neck out here, but given that NSF is funding this baby, I’m thinking she means that direct, whole-class, teacher-centered instruction is limited to smart students who would get it no matter how it is taught.

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“… encourage more students to engage deeply, work hard, persist and become more mathematically capable.”

High school? Too late.

Engagement drives hard work only if basic skills exist. Engagement has definite limits for driving mastery of skills that are no fun for even the most “natural” students. Fingering exercises, scales, and etudes driven by engagement? Nope. Love of Fantaisie Impromptu drives basic skills? Nope. Private music teachers know that it doesn’t work. It doesn’t work in sports and it doesn’t work in math. I thought it took me until Algebra II before I felt that I really had a good grasp of algebra – created from mastery of basic skills from nightly homework – which drove my understanding. It’s not the other way around.

There is no magic engagement path to mastery of skills, and skills drive understanding and success.

Success drives engagement, not the other way around.

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How would these ideas cause students to: “…engage deeply, work hard, persist and become more mathematically capable?”

How do you make hard work fun? Typically, we hear about in-class mixed ability group work using real world hands-on tasks. I haven’t read anything about how this should be done for individual homework.

A classic example I was involved with in my son’s fifth grade class was the First Lego League competition. This was supposed to be fun and engaging learning. I will leave alone that fact that students had to adopt roles (like researcher versus artist versus actually programming the robot) and not learn about any other area. I made sure my son was one of the two “programmers” on the team. He did not have any programming experience, but the goal was to have fun and learn by doing. Even with my “facilitating” (and more) the process, it wasn’t an effective approach. Sure, it’s exciting to see how quickly you can learn to make the robot move forward and turn, but that sort of rote learning is what many educators disparage. It’s not even equivalent to proper math textbooks that provide for the development of proper sequence of skills that tie the understandings from those basic skills into a larger and broader understanding of the subject by having them do all sorts of problem variations.

For the First Lego League, the goal was not building proper sequence of skills to learn about programming or robotics, but to get a task done for a competition. This is vocational education, not a general one. Note that this hands-on process accepts the fact that one can go from skills (doing) to understanding. Skills are never rote, but skills have to be carefully built for breadth and depth to learn a subject area. When this process is limited to just doing whatever it takes to get a job done – hacking – a proper and general understanding of a subject never happens.

When educators only look at what happens in class and ignore the needs of individual mastery of homework, they will fail. Engagement is always a good goal, but I’ve had a number of teachers and professors that have done that in a traditional setting. However, that engagement did not make nightly problem sets easy. There is no magic engagement bullet. Skills lead to success and success leads to engagement. Project-Based Learning is also skill-driven understanding, but it’s more rote and vocational than a traditional approach to education. Engagement make create some form of success, but not a proper education.

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Well said, Steve!

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