Adventures in Math!

That’s all well and good in practice, but how does it work in theory?

-Shmuel Weinberger

Things are looking up! If you’re a linear equation with a positive slope, that is… OK, no math jokes for me. For the first time in 12 years, I’m tackling an issue that’s been bothering me. What does it take to succeed in math education? A perfectly rational question… It’s taken daily practice, determination, and patience to find an answer, and I’m only getting started.

Resources in order of the SPECTRUM Acrostic

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Science…or math? “Wait,” I ask myself as I sit down to write my science and STEM education blog, “I don’t understand. This adventure is about… math?” Yes, math. “Except, isn’t this about adventures from a science teacher cultivating student-centered classrooms in STEM? Yes, and today we’re talking math. Math. Besides, “Mpectrum” doesn’t quite work, so let’s just roll with this.

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Dominic Walliman. dominicwalliman.com

Math, other than being the obvious character playing the “M” in STEM, is the language that science speaks. It’s the ball of sports – imagine trying to play football or basketball without the ball. One simply cannot do science without math. Science teachers use math to teach the math-y parts of science, like density or light years or population growth. Yet, at least in my experience, I don’t see a lot of science teachers who are certified to teach math or vice versa. Does this seem right to you?

This is a question I do not know the answer to. Knowing how involved teaching science is, I don’t automatically expect science teachers to get certified in math. Maybe they shouldn’t be. They are different professional disciplines, after all, supported by different administration and professional development conferences. They use different types of curriculum and are held to different knowledge and skills standards. As a member of several science education organizations, I can barely keep up with my own kind. Still, my heart aches as I hear math teachers complaining their students refuse to work on gravity “because it is science.” My man Einstein would, of course, disagree. I do hope there are science teachers like me who want to do more math/science integration and vice versa. More than any other combinations of subjects, I believe science and math need to be firmly integrated into teacher and student education. The trouble is, I have no idea where to start.

img_4580Once, through my alma mater at the University of Montana, we worked with the math education preservice teachers to build an integrated unit. Helpful exercise, sure, but it went unpracticed in the classroom and therefore quickly forgotten. Thanks to the direct integration of Common Core State Standards for Math through the Next Generation Science Standards, curriculum programs can better embed the needed math needed for each grade level in science. Yet that’s only for states that have adopted NGSS, right? Even with the uprising STEM education has established throughout the US, I’m concerned about the competency level a typical teacher needs to achieve to seamlessly combine subjects through a single unit, let alone with a whole school year.

Students measuring flag panels to scale in order to build flags for the exterior of the United Nations.

Students measuring flag panels to scale in order to build flags for the exterior of the United Nations.

The last couple months I’ve been working in several middle school math classes, humbled by 8th-grade linear equations and quadratic functions, rushed to recall distributive properties in 7th-grade algebra, yet relieved that two-step equations came back like riding a bike. It’s been awhile since I’ve completed these subjects as a student, let alone tackled as a teacher if not directly tied to scientific content. Do all teachers feel like this? I caught a break today and was able to work with students to calculate the composite area with each panel of various international flags as though they were ordering the material for manufacturing the exterior of the United Nations. Areas of rectangles, triangles, and circles…

Fortunately, STEM is a great place to start. Thanks to a gaining presence for STEM education and career awareness in recent years, I get encouragement from this push for interdisciplinary studies. Groups like the Maryland STEM Festival, National Environmental Education Foundation (NEEF), and professional development with programs like NAGT are doing a lot with effective integration.

Yet, I recently discovered with my very own eyes a disconnect between science and math middle school education. I speculate that we are widely varied in our competency levels for not just math and science integration, but STEM integration as a whole.

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What does a quality program for learning how to teach science and math look like? I recently came across a 7th class where science and math are combined. “Sometimes it’s double science, sometimes it’s double math, other days it’s separate. It just depends on what we are studying,” students explained when I asked them what their week looks like.

These magnet 7th grade students were conducting a collaborative investigation where they used shared data to answer questions on digestion including “What is the effect of being a vegetarian on calcium intake? Vitamin A?” “What is the effect of the average of weekly fast food on the average American’s fat intake?” and my personal favorite, “How does the time of day affect calcium intake in middle school? Carbohydrate intake?” They used Google sheets filled with anonymous data from their peers, Google slides to create presentations based on their data interpretation, and other multimedia to demonstrate their claim.

Closer to my answer, I met with their teacher and asked him what his goals were and how he thinks this type of approach can grow in the future. Mr. Greg Young, an administrator, and National Board Certified science teacher at Roberto Clemente Middle School in Germantown, Maryland, is in his first year of implementing the new science/math combined course for the campus. Because his background is in middle school education, with certifications in both secondary math and middle school science, he’s always approached science, math and engineering teaching with a combined focus. Before I forget, here is a Competency based curriculum, reflecting on practices in other countries than USA, just placing here for future notes.

“This is what I should be doing. [Since] we teach in such an isolated world, we are quick to forget that there is a world of millions of people trying to do the same thing we are. I know I’m hitting the right swings.”

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Soon, Mr. Young will begin an astronomy unit that will study the frequencies of radio telescopes and look at data from radio towers to prove the shape of the Milky Way Galaxy. Students will respond to a Request for Proposals to the National Radio Astronomical Association with to acquire time and data collection capacity on the giant telescopes. They will use multivariable quadratic equations and graphs to investigate measurable elements and molecules such as hydrogen, glucose, chlorophyll and water. It’s all part of the science of looking for life, “and we are looking at elements that are searchable through the universe. In all my prior teaching, I could imply a connection between subjects for students, but this is the first time I’m able to make a direct connection with them.I feel like I am at the beginning of a big wave.”

img_4578His students studying health in the example above were using overlapping skills for finding explanations in science and solutions in engineering. According to the NGSS Science & Engineering Practice “Using Mathematics and Computational Thinking,” they were using computers to work with large data sets and use mathematical representations (mean, mode, and median) to support or refute their claim. According to NGSS’ Appendix J, “During the middle school and high school years, students develop a number of powerful quantitative tools, from rates and proportional relationships to basic algebra and functions, to basic statistics and probability.” I like to make fun of science when I teach engineering. Context is everything, especially graphing and units. I always teach science with an engineering lens.”

Creating everything from scratch, Mr. Young is meeting all county benchmarks and students are completing their Quarterly Assessments for math and Common Tasks for science on schedule. He’s found lots of connections between the subjects, starting with bacterial and exponential growth and experiential design. When students are collecting their own data, and presenting it, they are engaged in inquiry – it doesn’t matter if they are in math or science. Students must explain standard deviation, p-value, and the overall value of their data in their statistical analyses. “Two plus two does not equal four. Two apples and two oranges do not equal four apples. Units are important,” Mr. Young reminds his students that numbers mean nothing without context and units of measurement.

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After primarily teaching science for 20 years, Mr. Young seems excited about the potential from this combined approach pilot. “I’ve always approached teaching from an integrated perspective, but have never had the opportunity to do both. I was always told that I should remain with one Professional Learning Community, either science or math. But not both,” said Mr. Young. “It wasn’t until last year, while at a training, that we just happened to have a conversation with the math chair, magnet center coordinator, and assistant principal that allowed us to begin this project.”

What about regular science and math programs on the same campus? While true integration has its merits, it might be more feasible to work with science and math teachers to create integrated units through the school year. What does your school do? What do you prefer? I want to hear from you.

I spoke with Mr. Ben Stano, a middle school math and science teacher, currently teaching 6th-grade science. On how to effectively integrate concepts and skills? “A good example of successful math integration in 6th grade science is using computer simulation with bar graphs with models of watersheds. It’s an easy interpretation from evapotranspiration to infiltration, and using simulations means they could easily check their own work. Arithmetic was not well represented, and I think it should be better represented.” When students reach for a calculator to finish their science assignment, “they are applying concepts without quite realizing it.”

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Integration does provide a certain flexibility and an approach that is likely teaching the teacher just as much as the students. “This is a drop in the bucket of what it could be if it’s done right. If you just give teachers a chance to naturally integrate and not segregate, there are lots of connections. We’ve spent so much time separating disciplines, now kids think that everything is different.”

When asked how he recommended for campuses to adopt this approach, he remarked, “it’s a structural philosophy that requires more than just teachers to get on board. It requires the support from the whole administration. I’m loyal to this campus, and it’s been loyal to me. I’ve never found a principal who was willing to try this before.”

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As for communicating the results from his research? “If I could communicate what we’re doing here, through a presentation of the data we’ve collected and gains among the students, then perhaps we could get district-wide encouragement to get more teachers involved. But we have to start with one school first.”

Both the US Department of Education and the National Science Foundation have Math Science Partnerships. Doesn’t this mean that there is funding available for more integration?

How would Mr. Young recommend young professionals proceed through this challenge? “Don’t quit. Don’t stop trying. I’m a bit of a stick in the mud, and I’m loyal to a fault. I will make it work here, this is the school where I started and will probably retire from 25 years from now. If I can convince my department chairs that this works out, show evidence of connections and successes, then maybe I can get another teacher to do it with me. Maybe I can start to build something.”

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As for me, I’m still stumbling along, teaching my various math and science middle school classes and helping out elsewhere when I can. I see students struggle, I cringe when I see math curriculum in standard measurements and science in metric. I regret not getting involved with this predicament 12 years ago when I got started in this field, but I like so many others got a degree and teaching certificate in science, not math. I’m just as guilty.

I’ve learned this. Provide context. No one can make sense of their world, or what you’re trying to teach them – be it music, math, history, English, PE, Spanish, or media – if they don’t have context. When we just threw the definition of density = mass/volume in front of those poor 6th graders in fall without coordinating the scope and sequence with the math teachers, we really did those kids a disservice. Perhaps with a bit more context, students can model this approach for us. This also goes for consistent units of measure, as Mr. Stano confirms, “This needs to be more cohesive. We could teach density AFTER students see the match concept, and we can put more thought into the science from a conceptual perspective. The logic that you’re asking to apply should match with the logic you are teaching them.”

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Since I have no idea where to start, I did some basic searches and included them here, both elementary and secondary. As always I’m including science/math/music by Herbie Hancock because this reference spans so many great topics. Somehow I found this blog, make what you will but it’s got some interesting headlines. And this newsletter has some great links to STEM organizations.

There’s so much more I wanted to cover in this adventure. Graphing, argumentation, assessment, solving problems (single and multi-step), and more. I realize now this is not an adventure, but an ongoing process in a journey unlike any other. I’ll be back, but for now I must move forward.

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