(This is the first post in a two-part series)
The new “question-of-the-week” is:
What are effective ways to use tech in math classes?
I believe that tech has a place in the classroom. I also believe it has to be kept in its place.
Every other week for the next month or two, this column will be featuring questions-and-answers exploring ways to use ed-tech in different classes.
The first academic discipline we’ll be targeting in the series is math.
Today, Bobson Wong, Elissa Scillieri, Jennifer Chang-Wathall, and Anne Jenks offer 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.
Response From Bobson Wong
Bobson Wong (@bobsonwong) has taught high school math in New York City public schools since 2005. He is a three-time recipient of the Math for America Master Teacher fellowship, a recipient of the New York State Master Teacher Fellowship, and a member of the advisory board for the National Museum of Mathematics. As an educational specialist for New York state, he writes and edits questions for state high school tests:
From clickers to calculators to online graphing tools, students today have access to a wide variety of technology to help them in math. Unfortunately, technology can be a major distraction if not properly used. Here are some ways that teachers can use technology effectively in a math class.
Foster student collaboration. Anyone who has seen a roomful of people silently tapping on their phones knows that technology can isolate people! Giving an electronic device to every student without fostering teamwork can stifle useful mathematical conversation. To get around this, students in class should work in groups of two or three per device so that they have to work together to answer questions.
Encourage independent work. Although student collaboration is useful, it’s also important to see how students work individually. If your students have internet access at home, many websites allow teachers to create assignments that students can complete at their own pace. Most of these sites can give hints to students and automatically grade assignments. DeltaMath creates individualized assignments for each student by giving similar problems with different numbers, so students can’t simply copy answers from a classmate. I often supplement homework with explanations, often from Math Bits Notebook and Purplemath, but also from other websites depending on the topic.
Guided discovery. Many online tools have guided discovery activities that can be used in class. For example, Desmos has hundreds of free activities (which are accessible through a web browser) that lead students through open-ended questions. Other websites like the Rossman/Chance Applet Collection or the random-number generators in graphing calculators help facilitate student discovery, especially for probability and statistics lessons where other methods of data collection are too time-consuming. The Wabbitemu app creates an exact replica of a TI-83 or TI-84 graphing calculator on Android mobile devices. (Unfortunately, there is no similar TI emulator for Apple devices.)
Quickly check student understanding. Not every lesson needs a full-blown activity. Teachers can use technology for quick formative or summative assessments—for example, as an in-class check, an exit ticket, or an end-of-unit review. Many websites offer fun, interactive ways to test students. For example, Kahoot! allows teachers to create their own online quizzes that students can access through their phones. Kahoot! allows teachers to type their own questions or import images—particularly useful for topics that have complicated math symbols or diagrams. In addition to websites like Kahoot!, teachers can also use classroom clickers, which range from free mobile apps to stand-alone devices that integrate with interactive white boards. Plickers is another interesting clicker-type app. Students hold up special paper cards (no electronic device required) that are scanned by a teacher using the Plickers mobile app, which records student choices.
Improve student accuracy. With auto-correct features built into almost every electronic device, students don’t have to be accurate to communicate. However, precision is critical to succeeding in math. Technology can train students to be more accurate. For example, DeltaMath is exceptional at this because the site requires answers to be typed correctly and doesn’t give partial credit for incorrect answers. I’ve found that many of my students get frustrated at having to enter information in the correct format to avoid being marked wrong, but the benefit is that they’ve become more careful in their work.
Most of the technology that I described above can be used on mobile devices, which will help students and teachers view phones as more than a distraction. Showing students how to use their mobile devices for math can help change the way that they view the subject. Best of all, much of the technology (including all of the apps that I mentioned) are free!
Response From Elissa Scillieri
Elissa Scillieri, Ed.D., is a math supervisor from New Jersey who considers herself a math missionary. She previously taught all subjects in the elementary grades before being offered the opportunity to share her enthusiasm for math with all ages. Follow her on Twitter: @EScillieri:
When technology made its debut in the math classroom, many teachers were excited about the math games that kept students engaged in practicing their skills. Students enjoyed playing them, and teachers appreciated the opportunity to help small groups of students while their classmates practiced through play. While that allowed for greater classroom efficiency, there was a drawback: These games often emphasize speed and only require students to practice rote math skills instead of their deeper mathematical thinking. Now that Chromebooks and iPads have become mainstays in the classroom, we realize the best uses of technology are those that do more than occupy students; instead, these learning tools enhance students’ classroom experiences.
Goal 1: Allow for curiosity without tedium
When students first learn how to plot points, they use paper and pencil to get accustomed to using a graph. As they further move into algebra, students are asked to use the graph to analyze lines and other figures. For example, a student or teacher might wonder how the graph of y = x -1 differs from the graph of y = x +8, but by hand each graph might take about five minutes to accurately complete. At this point, boredom overtakes curiosity, and students quickly realize that the act of wondering brings more work. On the other hand, the graphing tool at Desmos instantly creates each graph, allowing students more time to analyze and explore other ideas. The slider option on the graphing tool also addresses the question of what would happen on a graph for any number added to x. In so doing, these features encourage students to wonder and explore patterns without the fear that their curiosity will get them punished with more work.
Goal 2: To problem solve without calculation limitation
A few months ago, I worked with a group of middle school students on Dan Meyer’s 3-Act “Pyramid of Pennies” problem. While students were intrigued by the problem, once they realized that the final calculation would require a TON of calculations, they retreated back into their I-Hate-Math worlds. This particular group of students struggled, and they were sensitive about their weak computation skills. At first, they worked in groups and split up the calculations, and we allowed them to use calculators for assistance; however, even with the calculators, the work seemed overwhelming and repetitive. We needed a better way, so we worked together to put together a spreadsheet that would perform the calculations for us. Students were shocked at how quickly we came up with the answer by using a spreadsheet. They were eager to learn how to use a tool that would allow them to refocus their energy away from rote calculations. As we learned in working with this group, when offering students engaging problems, math teachers should give their students technology such as spreadsheets and calculators. These important tools free students’ minds so they can attend to the important work—the thinking behind the problem.
Response From Jennifer Chang-Wathall
Jennifer Chang-Wathall is an independent educational consultant, author, and part-time instructor for the University of Hong Kong. She has over 25 years’ experience as a classroom practitioner and she travels the world supporting schools with continuing professional development on Concept-Based Curriculum and Concept-Based Mathematics:
With the exponential growth in technology in the last decade, the integration of digital tools in the mathematics classroom has gained in popularity, and currently there are a variety of sophisticated ed-tech tools specifically designed for mathematics learning.
Tools that are designed to do and learn mathematics include dynamic software programs such as:
Computer algebra systems such as Maplesoft
Graphical display calculators, spreadsheets, electronic manipulatives, and applets
More generic digital tools that facilitate mathematics learning and teaching while developing 21st-century skills, such as creativity, communication, collaboration, and critical thinking, include the very powerful Googles Apps for Education (GAFE), and applications that give effective and efficient feedback on student progress such as Kahoot, Padlet, Plickers, and Flipgrid, to name a few.
Regardless of the tool, we must think about how the tool is used to enhance learning and not what the actual tool is. Four useful and practical models to support technology integration include the TPACK model, the PURIA model, the Triple E framework, and the SAMR model. Each model serves a different purpose to help you integrate technology in a more meaningful way with your students.
Stage 1: How do I assess my level of technological knowledge when combined with my content and pedagogical knowledge?
TPACK by Mishra & Koehler (2006) is a model that is useful for assessing your own levels of three different knowledge areas which are pedagogical, content, and technological knowledge of the teacher for successful technology integration. These three knowledge areas combine and interact to promote successful integration of technology strategies for the classroom and can be illustrated by a Venn diagram in figure 1, where the intersections of two knowledge and all three knowledge areas need to be considered for successful technology integration.
Teachers are encouraged to continually self-assess their own TPACK level while integrating educational technology. Here is an example of a rubric that could be used to survey the different knowledge domains and their intersections.
More examples of rubrics to assess TPACK can be found here
Stage 2: How do I become familiar with the actual ed-tech tool?
Another model developed by Beuadin and Bowers (1997) is the PURIA model, which is a framework that describes the different stages teachers go through when they learn about a new digital tool. The five stages of PURIA are: Play, Use, Recommend, Incorporate, and Assess. Learning to use and integrate a new digital tool into the mathematics classroom requires teachers to play with the tool first and then use it as an instrument for doing mathematics. The “Incorporate” and “Assess” stages encourage teachers to use the technology as a pedagogical tool while the “Recommends” stage marks the transition from mathematical to pedagogical aspects of the digital tool. Table 2 shows the PURIA model to support teacher’s development in terms of technology proficiency.
Figure 2 The PURIA Model: Play, Uses, Recommends, Incorporates, and Assesses: PURIA model. (Beaudin and Bowers, 1997 and extended by Zbiek and Hollebrands, 2008):
In the PURIA model, teachers progress to the next level once they feel confident about the current level. Levels do overlap, and teachers are encouraged to be self-paced while following this model.
Stage 3 How do I use the ed-tech tool in a meaningful way?
Another framework that supports teachers transformative use of technology in the classroom is Puentedura’s (2011) SAMR (Substitution, Augmentation, Modification, Redefinition) model. The four levels of SAMR represent a hierarchy of technology use, with new teachers often starting at the lowest level: the substitution level. This level may result in gains in efficiency; however, there are no gains in student learning. Examples include typing an essay instead of handwriting an essay. The next level is augmentation, which results in small learning and digital tools that are used in this manner adding functional value and improvement. An example of technology used at the augmentation level would be if students collect survey results using online survey tools. The ultimate goal is to encourage teachers to work at the upper two levels: modification and redefinition of the learning task. An example would be to ask students to create a video subject to peer feedback and editing. The way technology is used in this task provides increased multimodality, collaboration, and co-construction of knowledge and understanding. Figure 3 shows the SAMR levels and descriptions for each level.
The SAMR model. Source: Puentedura (2011), under CC BY-NC-SA 3.0 licence.
Stage 4: How do I ensure student learning is enhanced by an ed-tech tool?
The Triple E framework was developed by Kolb (2011) and is a model that helps measure how well ed-tech tools are supporting students to engage in, enhance, and extend learning. Figure 4 shows the questions you can ask yourself when using an ed-tech tool.
Several rubrics are available to assess lesson designs and any app or website using the Triple E framework. They can be found here.
The four models outlined: TPACK, PURIA, SAMR, and Triple E are useful when helping teachers develop the use of technology in a meaningful way and which ultimately enhances learning in mathematics. Regardless of the actual digital tool, how the actual digital tool is integrated to instruction and how the tool is utilized as a pedagogical strategy should be the focus of any successful technology integration in the mathematics classroom.
Response From Anne Jenks
Anne Jenks is an educator with 26 years of experience in teaching and school administration. She was the 2015 CUE Site Leader of the Year and the 2013 ACSA Region 13 Elementary School Principal of the Year. Currently, she is working as a consultant with an emphasis on ed-tech integration and STEM:
In our school, all students had 1:1 iPads. We were always looking for effective ways to integrate technology into the lesson design to maximize student engagement and outcomes and also to facilitate better instruction. We wanted to move beyond just using applications to teach basic math facts and came up with some creative ideas that had a positive effect on teaching and learning.
One strategy involved having teachers instruct students to use an interactive white board screencasting application on their iPad to record themselves as they worked on math problems. The teacher would find a multistep word problem that addressed math standards at that grade level. Then she would assign the problem and ask her students to use the application as they worked on the problem. They would use the application to illustrate the problem and record themselves explaining why they were doing what they were doing as they worked on it. Then, they would share the video with their teacher, so she could review their work. This was effective because if there was a problem with a student’s solution, the teacher could see where the student had gone wrong. She could then go back and reteach the concept and have the student correct the error.
Another strategy involved having students use Minecraft to show their understanding of decimals. They would illustrate the decimal by “building” it in Minecraft. This reinforced their understanding because the figures had to be constructed piece by piece. For instance, if they were working on hundredths, they would have to construct a figure using 100 blocks and then shade in the part that illustrated that particular decimal. Of course, this could be done using graph paper, but using a readily identifiable game increased engagement and was more relatable for the 5th graders.
We found project-based learning to be a particularly valuable way to integrate mathematical concepts in a meaningful way. In one instance, 4th graders were asked to redesign the playground. Part of this assignment involved having students draw the blueprint for the playground. The teacher used this as an opportunity to introduce basic geometric concepts and taught them how to find the area of a rectangle, square, and other shapes that they would use in their blueprints. Since this was part of a larger project with real-world implications rather than a “stand-alone” math lesson, the information became more relevant for the students.
The integration of technology in math instruction not only increased engagement and clarified concepts that could be abstract for students, but it also improved the teachers’ ability to discover when students were missing information and provide the appropriate remediation.
Thanks to Bobson, Elissa, Jennifer, and Anne for their contributions!
Please feel free to leave a comment with your reactions to the topic or directly to anything that has been said in this post.
Consider contributing a question to be answered in a future post. You can send one to me at firstname.lastname@example.org. When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.
You can also contact me on Twitter at @Larryferlazzo.
Education Week has published a collection of posts from this blog, along with new material, in an e-book form. It’s titled Classroom Management Q&As: Expert Strategies for Teaching.
Just a reminder; you can subscribe and receive updates from this blog via email or RSS Reader. And if you missed any of the highlights from the first seven years of this blog, you can see a categorized list below. The list doesn’t include ones from this current year, but you can find those by clicking on the “answers” category found in the sidebar.
I am also creating a Twitter list including all contributers to this column.
Look for Part Two in a few days.
The opinions expressed in Classroom Q&A With Larry Ferlazzo are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.