Category: Lab Posts

Labs as single concepts

9 Reasons for Using Spreadsheets in Schools

Spreadsheets are equity platforms available to all students at no cost. They can give every student a fresh start in math.
Spreadsheets from Microsoft, Google, and Apple are ubiquitous, easy to use, powerful, and part of a suite with common, familiar, supported interfaces.
Spreadsheets are the tools students will use in their workplace as well as school for relevant real learning.
Spreadsheets are not just computational tools, they are visualization and data science tools.
Spreadsheets are function machines using functions and functional thinking to build and work with models essential to all STEM projects.
Spreadsheets are the financial and business communities goto program, central to modern financial literacy.
Spreadsheets are coding platforms easy to use for beginners and powerful enough for serious programming.
Spreadsheets are sharing applications enabling and encouraging students to collaborate and community for group problem solving online.
Spreadsheets have a huge support network of videos, templates, and help available on the Web and the community.

Math as a Laboratory Science

Math is not only the last letter in STEM or STEAM, it is the only one that we do not picture as experimental. We don’t imagine students learning science without doing experiments. We don’t imagine them learning technology without writing code, or learning engineering without building models, or learning art without messing with paint, clay, or paper. Yet, we easily imagine learning math without experimenting. In fact, it is rare that students ever do a math experiment or think about math that does not have a “right” answer.

I learned to experiment from one of my great teachers, Walt Hunter. I even had the great good fortune to also being his chemistry lab assistant my senior year in high school. That I did not fall in love with chemistry was not his fault; I had just loved physics since I was 7 years old. But I did fall in love with experimentation, and like Walt I gained a deep belief that learning to experiment should be an essential aspect of every student’s education. I brought that belief to my physics classes replacing teacher demonstration with student experimentation. I took it to my Jr. High math classes, where I made my students worksheets that let them play with numbers and mathematical patterns. I carried it to my focus on manipulatives as a math coordinator, and I bring it to What if Math.

Using spreadsheets as basic learning tools for math has many advantages, but I think the most important one is that it turns math into a laboratory science. It enables students to experiment, to build and iterate models, to test those models, and to apply them to real-world data, complex rich data. It lets them ask and answer what if… questions. And it turns them into explorers who love to use math and who gain Walt’s experimental habits of mind, the thrill of discovery. It is this, I now know, that Lynn Steen saw when he described mathematics as the “Science of Patterns,” for math does belong to STEM/STEAM after all. So, when you plan your math classes, imagine your chemistry teacher, and the twice weekly labs where you learned to act like a scientist, to explore, to discover, to ask, “What if…”

Art

*Portrait of Antoine-Laurent Lavoisier and his wife by Jacques-Louis David, ca. 1788, Wikipedia

“Just try it on!”

Spanglish is one of those movies that grows on you. A coming to America story filled with themes that move us: a dedicated and resourceful woman, a dysfunctional but caring family, a highly successful artist, and of course love. It has many scenes that touch us deeply. One of those, highest on my list, is when Flor, who has just started as a housekeeper at the Clasky home, comes back to her own house after witnessing the mother embarrassing her daughter over her weight by buying her clothes a size too small. Flor, who had never learned English, asks, no she demands, that her daughter teach her how to say, “Just try it on!” They repeat it in synchrony over and over again. Flor arrives at the Clasky house before dawn to let out the new clothes, then she wakes Bernice up and holding up the clothes, she speaks English for the first time. “Just try it on!” “Just try it on!” she demands again and again until Bernice finally succumbs and the smile returns to her face.

I think of that poignant scene when I contemplate students and teachers in math classes today, for in conversations with teachers, parents, administrators, and yes students, I hear story after story about classrooms filled with kids who have given up on their ability to learn math, are just plain bored, or who see no reason to learn the math they are being taught. Teachers, who are themselves bored with a curriculum so heavily structured and predetermined it leaves no opportunity for creativity or even fun, try to pretend they are not. It is clear that teachers, students, parents, and administrators are dealing with a subject that no longer fits, a subject which has shrunken beyond recognition, a subject no longer relevant, no longer meaningful. Though, it claims to be conceptual, to enable students to learn to think and to solve problems, in reality it is mechanical in an age where machines have taken over most of those functions. It is too small for our digital age students and teachers who are wanting more, more relevance, more creativity, more fun, more learning. And it is too small for our classrooms where teachers want more discretion and more opportunities to engage.

In What if Math we have done more than just let out the old curriculum. We have started from scratch to build a digital age curriculum. Did we get it right? Do your students enjoy it more, learn more, feel better about their math ability? Are you having more fun? There is only one way to know, so I ask you, “What have you got to lose?”, and as Flor coaxed Bernice, “Just try it on!”, “Just try it on!”

Functional Thinking

We call our problem solving process, functional thinking. When we apply functional thinking to problem solving in the digital age, we find that a few fundamental models give us the tools to creatively solve quantitative problems. Think of functions as LEGOs, add columns using new rules, use outputs as new inputs, combine simple functions in new and creative ways.

1

Visualize the problem and set up parameter table with starting value x₀ and incremental Δx values (or in this case t₀ and Δt) of their inputs (independent variables), as well as the values of any “constants” that could be changed.

2

Organize your data into functions with an input, an output, and a rule connecting them.

3

Build and complete the model by adding additional functions and functions of functions.

4

Test and iterate your model to improve it and solve the problem. Add graphs, conditional formatting, or other data representations to design the output to communicate the results.

5

Now ask “What if…” I change this assumption, change the model, or input different data? Think out-of-the-box. Apply what you built to new situations and new problems.

Documents

Our slideshow

Our White Paper