Response: 'Tech Does Not Replace Pedagogy - It Complements It'
(This is the last post in a two-part series. You can see Part One here.)
The new "question-of-the-week" is:
What are effective ways to use tech in math classes?
In Part One, Bobson Wong, Elissa Scillieri, Jennifer Chang-Wathall, and Anne Jenks offered their recommendations. You can listen to a 10-minute conversation I had with Bobson, Elissa, and Jennifer on my BAM! Radio Show. You can also find a list of, and links to, previous shows here.
Today's commentaries come from Kristan Morales, Cathy Seeley, and Madeline Whitaker Good.
Response From Kristan Morales
Kristan Morales is a teacher at Chaparral High School in the Temecula Valley Unified School District in Temecula, Calif. She is a member of the Instructional Leadership Corps, a collaboration among the California Teachers Association, the Stanford Center for Opportunity Policy in Education, and the National Board Resource Center at Stanford. Connect with her by email or Twitter (@KristanMorales1):
Photo by Kristan Morales
My goal with technology is to support pedagogy that increases collaboration, critical thinking, creativity, and communication in the math classroom. I use technology and digital math tools at the "Transformation" levels in the SAMR model for technology integration.
The SAMR model. Source: Puentedura (2011), under CC BY-NC-SA 3.0 licence.
Here are some of my favorite tools for the math classroom:
Information Delivery System: Google Classroom
Pearson Textbook Resource: Math XL
Growth Mindset Math Activities: https://www.youcubed.org/
I integrate technology into my curriculum 2-3 times per week via Google Classroom. Students know all links will be posted there. I add the resource teacher as a co-teacher. Parents sign up for assignment notifications.
I use a Google Doc to keep track of classroom assignments and homework.
I have daily flexibility to change and adjust as needed. I keep this list current for students, parents, counselors, and SPED and AVID support teachers. Students and others can use Google Translate to access this document in multiple languages.
I assign a weekly Math XL homework assignment, a tech tool that is part of my current textbook adoption. I like the built-in supports such as "Help me Solve this problem," "Show me an example problem," "Show me a video." My students go back in as many times as needed to improve their grade. I also like that Math XL gives each student a problem with unique parameters. Partners can collaborate and help each other on the concepts and skills but, because their numbers are all different, each student must do their own work. I use Peardeck to give each student a voice in the classroom discussion. This tool is critically important for my shy students who normally do not like to speak up in class. It is a big upgrade from traditional white board responses where I see a lot of copy-catting. I start my year with growth-mindset activities. My students feel comfortable sharing on Peardeck and in the classroom because they know in my classroom "there are no wrong answers." Knowing that brain science has shown that mistakes actually grow your brain has freed them to share their thoughts.
In my lesson"Playdoh meets Peardeck," I teach geometric cross-sections of solids. Students use Playdoh to form solids and a knife to cut and discover cross-sections. They draw what they see on their paper and share their findings with the whole class on Peardeck. I use this model to crowdsource class ideas. After they chime in with ideas, we discuss as a whole class, identify correct solutions, and discuss why they make sense. Peardeck integrates seamlessly with Google Drive and automatically creates a student-reflection document after each session that can be used to extend the session to homework or further discussion.
Photo by Kristan Morales
I also regularly use Padlet for whole-class collaboration and sharing of ideas. Students post their ideas, solutions, and photos of their work. One thing I discovered is that when students know their peers will be seeing their work, the quality level goes way up! Here is an example of using Padlet. I asked students to design their own wedding cake using geometric solids and then find the volume of their cake.
Photo by Kristan Morales
Two more "must-have" tech tools for math teachers are Desmos and GeoGebra. Desmos teacher activities have a wealth of pre-activities suitable for all grade levels. Many are fun, interactive, and pair students up with others in the classroom. On the teacher dashboard, I can monitor live progress of student work and walk over and prompt struggling students with questions and one-on-one help to move them forward. Desmos activities encourage critical thinking and exploration in a way that is different from direct instruction. I require a Google Doc summary to accompany Desmos activities to extend the learning. The "Desmos Land the Plane" activity, which allows students to explore and apply linear equations, was a hit this year.
Photo by Kristan Morales
Since the Desmos Scientific Calculator is the one that students will use on the CAASPP test, I make it my in-class calculator so students get practice using it throughout the school year. I use the Desmos Graphing Calculator to teach graphing and properties of families of functions.
GeoGebra is another platform for graphing and demonstrating properties that has many classroom activities. For example, this year I coupled GeoGebra Rotating 2-D shapes to make 3-D solids with a Google Doc write-up where students explained their discoveries in GeoGebra.
Photo by Kristan Morales
The possibilities for tech integration in the math classroom are endless but remember: Technology does not replace pedagogy; it complements it and transforms learning in a way that was previously inconceivable without it.
Response From Cathy Seeley
Cathy Seeley (@CathySeeley ) is the author of Making Sense of Math: How to Help Every Student Become a Mathematical Thinker and Problem Solver (ASCD Arias 2016). Cathy has worked as a teacher, district mathematics coordinator, and Texas state mathematics director for grades K-12 and is a sought-after speaker, having spoken in all 50 states and around the world. A former president of the National Council of Teachers of Mathematics, Cathy recently retired as a senior fellow with the Charles A. Dana Center at the University of Texas, where she worked on state and national policy and improvement efforts, with a focus on P-12 mathematics:
In today's world of in-your-face technology everywhere we turn, it seems obvious that every classroom should be tapping into the power of technology to allow us to completely transform the way we structure teaching. This would seem an especially compelling assertion in mathematics, arguably the very foundation on which technological advances are based. I'd like to make a case for not being seduced by the bells and whistles of massive, comprehensive computer systems that precisely diagnose every type of mistake an individual student makes and offer up individualized remediation. There is certainly a role for these systems, especially if they supplement a student's regular math class. Let's consider first, however, a couple of mathematical tools that represent more focused and fundamental uses of technology.
First, I think every student needs access to an appropriate level of hand-held calculator or symbol-manipulation device, whether on a phone, a devoted computational device, or some other form of immediately accessible calculation. Basic four-function calculators can serve a useful role starting in the early grades. Students can explore number patterns that lead to conceptual understanding of operations and play with computation involving numbers that seem huge and mysterious to them. As students move through the grades, they might use a calculator as a tool when solving real problems with messy numbers, using technology to deal with ugly computations that might otherwise slow them down on their problem-solving journey. They can organize data and explore patterns in computation that lead to understanding important connecting mathematical ideas like equivalence and proportionality. And, as students begin to work with functions and algebraic representations, a device with graphing capabilities allows them to discover the kind of aha!s every math teacher loves to see—notions involving critical connections among representations involving graphs, numbers, tables, and symbols.
Even beyond algebra, we can now provide students with hand-held tools that help them organize and analyze data using sophisticated statistical tools that were once limited to only those who had studied statistics in college, bringing together what they know about functions and algebraic relationships with fundamental concepts of statistics. And more sophisticated tools will continue to be developed, perhaps even going beyond those that already offer ways to analyze symbolic expressions that cover the breadth of high school mathematics and beyond.
The second type of technological tool I consider essential for learning mathematics is dynamic geometric software. Computer software has been available for many years that allows students to easily construct geometric figures under various conditions (triangles with certain angles or lengths of sides, circles of various sizes, multiple geometric figures in various relationships and orientations, and so on). This software has revolutionized the teaching of geometry. When I was a student, it took considerable time and expertise to carefully construct equilateral triangles, angle bisectors, chords of circles, even true squares of particular side lengths. With the electronic ability to build not just one or two such figures, but as many as we might want, students can explore properties of whole classes of figures, while making and verifying conjectures across many cases. We can now make such tools available to all students not just with a computer but via various devices.
New devices and applications are being developed all the time, and there will always be a next best thing, whether a new tool to allow students to tackle more complex and relevant problems or new systems to help plan and implement instructional programs. My primary recommendation about investing in technology is to consider first the mathematical needs of teachers and students before investing in computer systems that help organize learning or manage student data. Just as we wouldn't want to try to teach science without lab equipment or engage students in sports without the proper gear, mathematical tools are critical in helping students learn the math they will use in today's world, regardless of what career path they might choose.
If we're going to use technology well, we need to learn how to incorporate the use of these mathematical tools into our teaching. Reflecting on the mathematics we teach in elementary and secondary schools, Henry Pollak, a well-known applied mathematician, has suggested that the emergence of technology has made some mathematics less important, some mathematics more important, and some mathematics possible that we could not have dealt with before.
Calculators and time-saving technological devices are pervasive outside of school. Let's not pretend they don't exist when we're inside school. Let's not insist on teaching students all the computational skills a calculator can do before we allow them to use one. Instead, let us help them learn when to use a calculator or other device and when it's better, faster, and easier to just figure something out with a pencil or, even better, in their heads. Let's use all the tools and resources we can to give students opportunities to solve more interesting and relevant problems than they would otherwise be able to tackle.
Response From Madeline Whitaker Good
Madeline Whitaker Good has taught elementary and middle school and is currently a middle school teacher in Springfield, Mo. She is a co-author of Your First Year:
Using tech in math classes is such a topic subject for me personally. Math is a subject that has aspects that simply must be done by hand to be the most effective. Some skills do not require this, but many do, especially as students learn math that is more and more complex. Also, by the time students get to 8th grade, if they find themselves in a free-for-all tech-centered classroom, they will quickly learn that there are magical online calculators that will solve many problems for them! Yes, we want math teachers to be giving students problems that don't have one clear answer, but in reality, sometimes you need to just solve a two-step equation. Or find the slope of a line. Or calculate the volume of a cylinder.
Tech goes wrong in a math classroom when teachers rely on it too heavily and too soon in a lesson. If students do not have a grasp of how to solve that day's topic, and they are given unlimited access to online problems and tools, I have found they are much more likely to make mistakes during problem-solving (since they don't show their work as much) and they are much more likely to rely on online calculators to give them a quick answer. This is especially true when you are working on a topic that does have one-answer solutions. Obviously there are exceptions to this, and much of it depends on the teacher and the topic, but in general, I have found this to be a consistent pattern in my teaching.
With these issues always in play in a math classroom, I have learned that the most effective way to use tech in a math class is to use it purposefully in structured ways that help extend student learning. For example, I love using tech for review activities (Kahoot, Quizlet Live, online math games). In these situations, I know I have already taught the content and made it accessible to my students, so they will be less likely to feel the need to use the magical online calculators. Also, once students are relatively comfortable with a topic, showing their work becomes almost second nature to many of them. By using tech in purposefully structured ways, you will find that both you and your students benefit from it greatly.
Thanks to Kristan, Cathy, and Madeline for their contributions!
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