Reforging the Math Curriculum through Computer-Based Math: An Interview with Craig Hane
Today we have an interview with a special guest: Craig Hane, multi-book author and creator of a unique math curriculum that uses computer-based math. Read on for his thoughts on teaching, information about his curriculum and the ways in which Wolfram|Alpha can help math learners. This interview has been edited for style.
Craig Hane has been both a student and teacher of mathematics for many years. Earning his PhD in algebraic number theory in 1966, he’s spent decades sharing his love of math with countless students. He began teaching as a math professor before connecting with another student group: trade workers.
In the 1980s, he developed applied mathematics training for technical, hands-on fields. Those trainings would later shape his company Triad Math Inc., as well as help to provide the basis for a curriculum known as Golden Rule Math. Since 2011, Hane has been helping all kinds of students through his various programs.
Do you have a philosophy of teaching, and if so, what is it?
My “philosophy” is probably best explained by part 1 of Golden Rule Math for All God’s Children (abbreviated GRM), what I call the “Four Essential Ingredients of an Optimal 21st-Century Math Education”:
- “SPIKE Pedagogy”
- Proper content
- Good teacher
- Good coach
When these four “Essential Ingredients” are achieved, virtually any student can, and will, learn the math they need to empower various future ambitions.
For those who haven’t read your work, what is SPIKE Pedagogy?
“SPIKE” is an acronym for the following: Self-Paced, Proper Content, Interactive, Keeping score, Empathy and Humor. Every student will learn at his or her unique pace for many reasons. With modern technologies, this is possible, as I do it in Triad Math’s Six -Tier Math Program.
This is a very brief description of SPIKE. For a more in-depth treatment, you can visit my website and click the “How and Why…” link.
You’re working on several ongoing projects, one of which is your Golden Rule Math curriculum. Could you give a short explanation of what makes this curriculum unique?
The GRM curriculum, which consists of “Six Tiers,” achieves all of the first three Essential Ingredients and makes it possible for a non–math teacher to be a good coach. I also teach how to be a great coach in chapter 1.4.
How did you end up focusing on Golden Rule Math in particular? What drove you to work on this curriculum?
I have taught math at all levels for many decades utilizing the four Essential Ingredients when tutoring one on one. It is impossible to do this in a group setting with high-school math.
By 2008, technologies had developed to where this could be possible to do online, sort of like Khan Academy tutorial videos. But you also need quizzes and notes and exercises, a learning management system, a forum to answer questions and then a proper sequence of topics (i.e. proper content). Now I can teach math to a remote student the way I would want math taught to me if I were a student. Thus, Golden Rule Math.
In 2009, Wolfram|Alpha revolutionized how a student should learn and practice math for STEM subjects. I developed the Six Tier Math Program that not only now could deliver SPIKE Pedagogy, but also utilize Wolfram|Alpha for proper content. You need to start any student with a good foundation, which lets them understand how integrated math subjects are.
For a foundation, a student needs to learn practical algebra, geometry and trigonometry, utilizing a scientific calculator for arithmetic calculations. This can be done in about one semester for most students. Think about this! What math program being taught by our current schools lays such a foundation? I find at least 80% of students can master this foundation and develop confidence in their ability and self-esteem.
The good psychology of a student is a necessary prerequisite for success in math. This foundation also transforms students who are afraid of math or dislike math and who have failed with the old 20th-century standard math curriculum into successes. It is becoming a huge success with homeschool students who have the freedom to achieve such a foundation.
What sorts of challenges and successes have you seen with students learning through Golden Rule Math?
Just successes. The challenge is to make the Six Tier Program available to math students. Mostly this has been done with homeschooling. Regular schools do not want to transform for obvious reasons. For me, the GRM curriculum makes the current math textbooks and standardized tests and group pedagogy, i.e. the classroom, all obsolete.
Current math programs are kind of like Kodak photography and the GRM program is like digital photography, to use an analogy. Another analogy is that current math programs are like teaching carpentry with manual 17th- and 18th-century tools, and the GRM program is like teaching carpentry with modern electronic power tools and computers.
Why did you decide to incorporate Wolfram technology into your curriculum, and what benefits have you seen from using tools like Wolfram|Alpha?
It’s a power tool versus manual tools. Wolfram|Alpha is an amazing tool. It seems like magic to me. It is more dramatic than the scientific calculator was to the old slide rule. Now a student can master calculus in about one semester, and the difficulty of integral calculus goes from about an 8 on a scale of 1 to 10 down to a 2.
Integral calculus pre-Wolfram|Alpha was a major barrier for STEM students. The concepts are easy. The manual tools — i.e. finding antiderivatives called techniques of integration to apply the fundamental theorem of calculus to evaluate definite integrals — are very difficult to master, and they often can’t solve the problem.
Wolfram|Alpha solves any such problem quickly and easily. Now a student can do many more problems and learn the concepts much better. Differential equations, same thing only more so. The best way to master a concept is to do many example problems. With Wolfram|Alpha, you can do 20 examples of a type of problem in the time you could do only one manually, if you could do it at all.
You can also do problems that can’t be done manually. For example, the antiderivative of xSin(x²) can be done manually, but Sin(x²) cannot. So, you won’t find Sin(x²) in a calculus book, although you need to be able to solve it for some science or engineering situations. Wolfram|Alpha does them both immediately! –.5Cos(x²) is pretty easy to find for the first, but a special function called a Fresnel integral is the answer to the second. Not easy to find and not taught in most calculus courses. Indeed, a special function is an infinite series, and Wolfram|Alpha tells you the first few terms.
What would you say to someone who says they’re “not a math person”?
Math is a universal language. So, this is sort of like saying someone is “not a natural language person.” Hmm. Hard to communicate.
Virtually any student can learn math when it is taught the GRM way. Very few students can learn math properly when taught the old way. Simply try my Six Tier Math Program, and you will find you can understand math, and probably enjoy it too. If not, there is no charge.
Where do you see the future of math pedagogy?
SPIKE Pedagogy. It is 10 times better than the current pedagogies being used by our schools.
Do you think there will be a shift toward more computer-based math classes?
Yes. As soon as enough students are succeeding with the new SPIKE Pedagogy and math programs, it is unavoidable. It is sort of like how the scientific calculator, in 1972, made all the log and trig tables and slide rules obsolete.
Computational thinking is undoubtedly a 21st-century skill. How do you think anyone, not just students, can learn to think more computationally?
Define “computational thinking.” If you mean utilizing math concepts to understand processes and situations, then I think tools like Wolfram|Alpha are the keys to success.
For example, statistics can be taught much easier and better with modern tools. SPC has been revolutionized by SPC for Excel. Spreadsheets have revolutionized accounting. Wolfram|Alpha revolutionizes many math tools. Calculus and differential equations are just the tip of the iceberg.
The Wolfram Language now makes it possible, and easy, to integrate databases with math programs. The Wolfram Language is, in my opinion, the first programming language a student should learn. Learning Wolfram|Alpha may be a good first step.
You’ve used Wolfram|Alpha in some of your other projects, including Dr. Del’s STEM Math Club, which connects to your nonprofit helping students with STEM-related mathematics. Could you share a bit of information about this program?
I have developed a Six Tier Math Program for Triad Math Inc., which utilizes modern 21st-century technologies like Amazon’s AWS and PoD, Moodle, Mailchimp, WooCommerce and others. This program is delivered with SPIKE Pedagogy. Most significantly, it utilizes Wolfram|Alpha to destroy the math barrier for STEM math subjects like precalculus, calculus and differential equations in Tiers 4, 5 and 6.
This program is also available via Dr. Del’s STEM Math Club for schools or students to simply supplement and augment a good math program they are receiving at a school. Any student who is at all interested in a STEM subject should join. Visit here to learn all about it.
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Thanks to Craig Hane for sharing his story and his work. For more information, please explore the links in the interview and visit his website here.
About the blogger:
Jesika Brooks
Jesika Brooks is an editor and bookworm with a Master of Library and Information Science degree. She works in the field of higher education as an educational technology librarian, assisting with everything from setting up Learning Management Systems to teaching students how to use edtech tools. A lifelong learner herself, she has always been fascinated by the intersection of education and technology. She edits the Tech-Based Teaching blog (and always wants to hear from new voices!).
