The Friday Fave took a week off for the big math conference, but is back in
action and ready to go with a brand-spanking new activity:
Battle Boats.
It’s coordinate-grid practice in the form of a game. Fire away! The
results of your tries will teach you something about the location of your
partner’s boats. Can you reveal your partner’s boats before they
reveal yours?
IMPORTANTNOTETOTEACHERS! You’ll need to orchestrate a little
real-world device (or seat) swapping in order to make the game go. Full
instructions in the Teacher Tips and the activity.
While your in a Cartesian kind of mood, you might also have a peek at these
other grid-based activities:
“Beta” means this product will continue to change in ways small
and large. “Beta” means we’re in the process of creating
helpful documentation, tutorials, and examples. “Beta” means we
don’t warranty this product for your classrooms or presentations just yet, and
if you use it in those contexts you should offer lots of assistance along with
all of these disclaimers.
“Beta” also means we want your feedback. (Send email to feedback@desmos.com or
tweets to @desmos.) What features do you want? Do you see sharp edges that
need sanding? Tell us what you like and, more importantly, what confuses or
surprises you. Your feedback makes us and our products stronger.
Our goal is to release our geometry tool without the “beta” label
sometime over the summer, right in time for the start of the 2017-2018 school
year in North America. Even at this early stage, we wanted to let our users
know why we’re building this product, and how we envision its integration with
the rest of our toolset.
Why did we build geometry?
We grew up as students of interactive geometry software. Pioneers like
Geometer’s Sketchpad
and Cabri laid the groundwork for an
entire industry. Other tools, like
Geogebra and
Euclidea.xyz, have since emerged with
their own unique perspectives, strengths, and weaknesses.
Given this wealth of great existing technology, why did we choose to build our own?
First, our goals are different than those embodied by most of those other
tools. When we design products, we design first for students who struggle with
math and we assume they may also struggle with technology. We strive for a
student’s first creation with our tools to feel effortless and joyful.
For that reason, our geometry tool has a far shorter list of features than
some of those above. We will carefully expand that list over time, never
trading power for ease-of-use.
Second, we wanted a geometry tool that integrates cleanly with the rest of our
products. We wanted a lightweight, blazingly fast, browser-based tool. We
wanted a Geometry API for
partners that closely resembles our
Graphing API. We wanted a tool that
could fit neatly inside of our
Activity Builder.
We don’t intend our work in geometry to replace the existing set of
interactive geometry tools, but rather to supplement them. We hope our work
will open up the magic of synthetic geometry to millions of new students.
Will geometry be free?
Yes. Our geometry product will be completely free, now and for as long as we
support it.
We can’t promise that Desmos will always exist (though we promise to
try!) nor can we promise that we will always support any given product. (As a
small organization, focus is critical and we can only support products that we
believe have the biggest impact.) Our promise, instead, is to never move any
of our free products behind a “paywall.” We won’t ever
charge you for products that are free today.
We can sustain that promise because we’ve partnered with organizations
who license our products for commercial use. Those organizations – dozens of
them, both large and small – get access to our APIs, which makes it possible
to integrate our technology into their programs. They also get access to the
knowledge and experience of our team. Partnerships fund our growing business
and allow us to keep our products free for teachers and students.
You’ll soon see our geometry tool in products from organizations like
Pearson,
College Preparatory Mathematics, and
Kendall Hunt. If you see one of
those products, give it a good, critical evaluation. We only work with
ambitious partners who care deeply about teachers, students, math, and
technology. And if that sounds like your organization, please email an
introduction to
partnerships@desmos.com.
This week we asked the Desmos Fellows to find the errors in
this
five-screen Pythagorean theorem practice activity, where the errors were
violations of the
Desmos activity building code. The fellows had much to say about each screen in general, and even more to
say about the activity as a whole. Check out their analysis below.
Screen 1:
Anna Scholl noticed that
this screen presents the formal definition of the Pythagorean theorem before
students are asked to do any informal thinking around the concept.
Scott Miller noted that the
prompt reads and sounds like a video tutorial. This violates the Desmos
principle to keep expository screens short, focused, and connected to existing
student thinking.
Jenn Vadnais thought that the
sketch feature was used inappropriately, and that showing work using the
sketch tool can be challenging for students.
Screen 2:
While Screen 2 wasn’t the biggest violator,
Patty Stephens called out a
missed opportunity to connect visual representations to algebraic and
numerical representations.
Screen 3:
Linda Saeta noted that this
screen asks for a numeric answer, in which case the sketch adds very little
except to verify that the student can draw a right triangle. While generating
your own representations is a valuable problem solving strategy, it’s not
clear how drawing these images in the sketch screen will benefit student
learning. Bob Lochel adds to this:
“My concern is that we are presenting students with an algebraic means for
finding the length of the hypotenuse on Screen 1, but then insisting on Screen
3 that students sketch the triangle as a justification. If we have achieved
buy-in that the formula is sound and necessary, then why are we still
sketching triangles as part of practice?”
Screen 4:
Allison Krasnow thought the
animation on Screen 4 had nothing to do mathematically with the problem or why
the Pythagorean Theorem is true, adding that, “It just makes me want to plug
and chug til I get the right side length instead of using math.” When building
activities we should be careful not to include screens where students can
complete the task through guess-and-check, without thinking mathematically.
Screen 5:
Suzanne von Oy asks the question,
“Was there any benefit at all to using Desmos for these problems?” Allison
Krasnow shares this concern, noting that Screen 5 asks for a simple
right/wrong answer, which is unlikely to lead to rich discussions.
Overall the sentiment was that the use of Desmos didn’t add much, if at all,
to the paper version of this practice activity. When creating activities, Jenn
Vadnais keeps in mind that “the interactive nature of Desmos draws students
(and adults) into the math. People love causing math to happen within the
Desmos platform and that aspect was missing.” The fellows didn’t give up on
this activity entirely, offering a couple of simple ways to improve it such as
creating opportunities for conversation through an error analysis problem or a
problem where there are multiple ways to be right or wrong.
