Integrating Technology into a Math Lesson

“I’m petrified that we’ll apply new technology to old pedagogy,” Professor Elliot Soloway at the University of Michigan said…. “We are not exploiting the affordances of the new technology to give kids new kinds of learn-by-doing activities….What a waste!”

Soloway expresses in vivid language a fixed belief among many high-tech advocates that new technologies such as tablets, smart phones, and similar devices can be used to transform traditional  teacher-centered instruction into progressive, student-centered learning-by-doing lessons . When these devices, however, are used to maintain existing pedagogies, it is a “waste.” Perhaps. Here is a math lesson I saw a few weeks ago. Would you  agree with Professor Soloway?

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In the charter school I visited, the Geometry class of 29 students, mostly Latino with a sprinkling of other minorities and whites, had already begun the  lesson when I arrived. Students sat sitting in seven rows of four desks each facing white-boards and a screen. Inspirational quotes, student work, and math-related posters dotted the walls.

The objective for the day’s lesson was written on the white-board: “I can calculate surface area and volume of spheres.” On the other side of the white-board were listed school rules and a staircase of escalating consequences. Below the lists was the agenda for this lesson:

1. Launch

2. Presentation

3. Practice

4. Conclusion

5. Exit Ticket

Each student has a four-page worksheet with “launch,” “presentation,” “practice,” and “conclusion” on it. At the top of each page was typed: “I CAN calculate the surface area and volume of a sphere.” On the “launch” page there were multiple questions on a basketball such as “The amount of leather used to make the outside of the ball represents________________ because ______________.”[i]

I arrived during the “practice” part of the lesson.

The teacher was leading students through questions on the worksheet: “Find the approximate SA (surface area) and volume of the following sphere.” A picture of a sphere is on the worksheet with a dotted line across the diameter marked with “18 m.”

The teacher walked up and down the rows with a constant patter about the problems students are working on: “I like that idea,” he said to one student, “show Christian your solution; I think it will show that it is efficient.” At one point, he says to a student: “I challenge your calculation. Show me how you did it.”

The teacher claps his hands in quick rhythm and brings the activity to a close. Students stop. He then says: “Let’s see if you guys know what you are talking about?”

The teacher now goes to the Exit Ticket part of lesson, a software app that teachers had designed for classroom use with recycled iPods. Students get their mobile device and login. The teacher gives them a new problem to solve and students go to work on their devices. “Definitely use your notes for the formula you put down,” he tells the class.[ii]

Holding an iPad with software that monitors students’ work on their recycled iPods, the teacher walks around answering student questions and making comments: “You’re annotating makes me happy. I love the evidence I’m seeing.”

He stops and answers a student’s question. He then asks class, as they are working, “How many of you did I have last year?” About half of students raise their hands. “Wasn’t I a royal pain in having you line up items as you write up a problem and its solution? When you get to college, you leave out a symbol, a semicolon, you torpedo the entire solution.”

As he scans the classroom and looks at his iPad to see what students are doing, he turns to a student and says, “Alex, we’re talking math; that’s your warning.”

Teacher claps again. “Let’s move to ‘Conclusion.’” He tells class: “Read the problem silently and after 3 minutes, talk to your neighbor on how you did it.” Another quick handclap. “Let’s do another poll on answer. Students use their iPods. “OK,” teacher says. “Ten voted for this answer and two voted for the other. The two are correct. Why are these two right? Check with your neighbor. Talk it out”

There is a noticeable surge of energy in the class after the teacher pointed out the error. Pairs of students talk to one another. Teacher waits and then says: “Alex, explain the answer.” After Alex talked through the explanation, teacher claps hands and says, “Eyes up here.” He goes over the homework and reminds students of test in two days. Bell rings but teacher holds class until all of the iPods are returned to the tray in front of the room. He lets class go when last one is returned.


[i] Leadership Public School (LPS) teachers had designed readers for various courses including this Geometry class; these readers contain lessons and accompanying worksheets with problems and questions. Full disclosure: I am a member of the LPS Board of Trustees and have visited classrooms in all four LPS schools.

[ii] Exit Ticket was designed by teachers at LPS. Using recycled iPods and cell phones, students could point and click on answers on a screen. Because they were iPods, students used other functions beyond the “clicker” one. Teachers wrote the apps for the devices  to use for instantaneous feedback from students.

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25 Comments

Filed under how teachers teach, technology use

25 responses to “Integrating Technology into a Math Lesson

  1. Pingback: Integrating Technology into a Math Lesson by larry Cuban | E-Learning-Inclusivo (Mashup) | Scoop.it

  2. Pingback: Integrating Technology into a Math Lesson by larry Cuban « juandon. Innovación y conocimiento

  3. I teach in a school that just got a 1:1 iPad program this year and this is a question I struggle with daily as a math teacher and tech enthusiast. I’m not sure if I should be using the technology to enhance my current practices or if I should be fundamentally changing the way I teach. On the one hand, the technology allows me to enhance my teaching. I can get responses instantly from students and intervene quickly. Students can do assignments online and get instant feedback and even have links to resources to help them navigate the challenges. However, I can’t help thinking that this new technology is affording us a real opportunity to fundamentally change the way we teach and prepare our students better for the 21st century. It seems like the technology has the power to help us differentiate like never before to make sure each student is truly learning at his/her level. Also, it allows students to collaborate not only amongst themselves but also share ideas and collaborate with people from all over the world. A major restraint is a lack of know how. It’s only my third year in the classroom and a tech enthusiast and it took a major mindset shift to switch to 1:1. Based on research, Dr. Cuban, teachers aren’t getting prepared to integrate technology in their classrooms or to teach in truly fundamental different ways, which makes sense because schools haven’t moved in this direction.

    • larrycuban

      Jin-Soo,
      Thanks for your comment about your efforts and where you think the problem is located:both in teacher education institutions and the ways that schools are organized. At least that is what I get out of what you say. It took you three years and a “major mindset switch” to use 1:1 and you characterize yourself as a “tech enthusiast.” Strikes me that there is something about schools as they are currently structured and teacher work situations that allow for little collaboration to deal with these issues that have a lot to do with what you describe.

      • Hello Dr. Cuban,

        I think you got it right about teacher training and the organization of schools. There’s not much incentive to take risks. Why not stick to what’s tried and true? Students are still learning after all. Especially in schools that have not met AYP, the focus on standardized tests reduce the incentive to innovate further. The tests don’t assess how deep a student’s knowledge of skills are so there’s an incentive to teach concepts superficially. Perhaps Common Core will address this.

        Also, just for clarification, it didn’t take three years to incorporate 1:1. Rather, my school got a grant for 1:1 ipad implementation this school year. I am encouraged that this wide scale implementation facilitated increased teacher collaboration because we were all implementing these new tools together. Also, really encouraged by the collaboration happening between teachers on the web.

        I still would like to think that these new technological tools present an opportunity to rethink what schools look like, the role of teachers, the role of students, and what learning looks like. Do you think it’s possible for this kind of questioning to happen in traditional public school districts or will this kind of experimentation more likely come from charter schools?

      • larrycuban

        Jin-Soo, I not only believe but actually know that the kind of questioning you seek does occur in both traditional and charter schools. Not many, mind you, but it does occur. Occur, of course, does not mean adoption of new structures and organization, and adoption–as you know–does not necessarily mean implementation as intended. So even questioning is only the first step of a long trail. Thanks for commenting.

  4. Cal

    I really hate the jargon, and the absurd distortions teachers go through to avoid saying “Hey, you made a mistake” or “oops, you went the wrong way”. “I challenge that calculation.” Seriously? Who says that? He’s the teacher, he’s the expert. He’s not challenging it. He’s saying hey, you made a mistake.

    I used to get very irritated at ed school when we were told to send students the message that “mistakes are okay” (which they are) but at the same time, never ever say “that’s wrong”. If mistakes are okay (and they are) then why go through language gyrations to avoid saying “that’s wrong, you made a mistake”?

    Add in the nonsense about “voting” for the right answer. It’s not a frigging democracy. The kids selected an answer. Most of them were wrong. Spot the error they made. (interesting that the error rate was that high, by the way. Leaving aside technology, most of them weren’t getting it.)

    So far as the technology goes, most students simply don’t have the interest or the ability to learn by doing. They need practice and direct instruction, and any technology that allows the teacher to assess the room is good. I would prefer something that wasn’t always multiple choice, though. In fact, that’s the next thing I’m going to be working on, to see if I can create some sort of app that students could send me the answer quickly via text and I could get the results in some sort of formatted way.

    • larrycuban

      As always, Cal, thanks for your candor.

    • bellce0

      Good points, Cal. The contrived teacher language often associated with effective classroom instruction irritates me as well. Mistakes are an important part of all learning processes, but it is essential to know when to simply say, “No, that is not correct.”

    • I think the purpose of having the kids vote for the correct answer is to highlight two issues: 1. that many students probably have an incorrect response, 2. It forces every kid to at least think far enough to be able to choose an answer. Too often children hide away in their individual corners of the room and spend their thinking time in class on “how can I avoid being made to look wrong?”

      There is an interesting theory that Dr. Peter Liljedahl has recommended – when the students ask questions, try and ensure that they spend more time thinking, rather than less. He says that children ask questions which stop their thinking, and that one should be careful how these are answered. You have no doubt noticed that children ask questions when you are near them, which end up interrupting their flow of thought, and which they do not need the answer to (since if you were not around, they would have likely figured it out themselves). Stop answering “proximity” questions, and you’ll force children to think more. (This does not mean that when you are near a child and you see that they are struggling to the point of giving up that you can’t interject on your own and offer assistance).

      Children also ask questions like “is this right?” Since we want them to be able to answer that question themselves, he recommends either not answering it, or answering it with some guidance as to how the child can determine for themselves if they are correct.

      These techniques should probably only carefully taught to in-service teachers, if at all, since they may get the message, “Stop answering questions students ask” instead of the more thoughtful “Be cautious when answering certain types of student questions.”

      • larrycuban

        Dealing with student questions is, indeed, tricky, David. For me, you make important distinctions on managing questions to encourage thinking. Thanks.

  5. I think this is a horrible example of “integrating technology into math.” It includes all of the wrong notions as to what “doing mathematics” actually is. Calculating the surface of a sphere is not mathematics, it is a calculation. Using that calculation in some context, or to solve a problem is more like mathematics. Developing a procedure and abstracting from a set of data to a general rule is doing mathematics. We have far too much ‘learning calculations’ in mathematics classes, and not enough ‘doing mathematics.’

    Today I taught a teacher how to use Excel to create graphs, and generate data from the compound interest formula. In order to use Excel for this purpose, you have to understand that at its heart, compound interest is about the application of percentages recursively applied to a growing principal. The core mathematical concept is left intact through the application of this technology. However, the consequence of using the technology here is that students can change the interest rate, change the initial capital and immediately see the change in the overall result. Instead of looking at a few examples painstakingly calculated by hand, students can generate dozens of results within a few minutes and much more quickly see the relationship between interest rates and principal.

    Similar examples can be applied to graphing, geometric solid, etc…

  6. Philip Crooks

    Here in Australia the Federal government has given money for all year 9 and 10 students to have a laptop. My school has gone with Macs it must have cost a fortune and what a waste of money. None of the teaching staff have one were not even offered one. No training with the Mac just given out. Mad. There does seem to be an idea that a laptop will some how teach the children, god knows how. But politicians and parents like bright shiny things so we waste money on them.
    I tried to use them with a class. What happened? I’ve left mine at home mine is not charged mine is broken mine was taken off me because I went on facespace or had down loaded music.

    • larrycuban

      The truth is, Philip, that I hate to hear such stories. Not consulting with teachers beforehand is dumb enough but not to give teachers a laptop stretches dumbness into organizational stupidity.

  7. It’s encouraging to hear teachers owning such success at their school. I do have questions about their future plan. The reason that the pedagogy comes into question when thinking about integrating technology (Wenglinsky-style) is partly because of modern devices “can” provide better mental models (especially for math and science) that can be embodied (a la Barsalou or Black) and/or provide opportunities for situated learning (Dede). We need those apps to come out sooner rather than later. In absence of those apps, I’m glad that at least it’s making classrooms more efficient with frequent formative assessment. Although, I can’t tell the quality of feedback that students are getting. On another note, those math teachers might want to combine Dan Meyer’s new technique of using videos to hook, in the beginning of the lesson.

  8. Well,
    Having been at this for quite a few years…and suffering with the pace of change…and seeing many classrooms where technology is not used in a transformative way, I am going to choose to highlight what I see as positive in this lesson description.
    Let’s be clear first that I have been influenced deeply by the work of Seymour Papert and Elliot and others, who have been encouraging more student directed initiatives and promoting a ‘learner’s stance’ and ‘student in charge’ etc. If my following comments give you cause to doubt this, please check what I have written in The Construction Zone blog. (Not trying to push you there – just contextualizing what is going to appear to some as support for the implementation above. )
    Despite the somewhat militaristic and controlling tone in this lesson, there are a few things that serve the kids well:
    1. There is clarity of purpose (oh, I know it’s not student-generated – but it is a clear well, articulated goal). The kids know exactly the intended outcome.
    2. Teacher says, “I like that idea,” he said to one student, “show Christian your solution; I think it will show that it is efficient.” This is supportive and encouraging of distributed expertise and positive peer interaction.
    3. He says, “I challenge your calculation. Show me how you did it.” If his tone of voice is playful, this is ok to get the student to tiptoe back through his/her thinking to explain and demonstrate or, to consolidate, understanding.
    4. He says, “You’re annotating makes me happy. I love the evidence I’m seeing.” He doesn’t give false praise. He is telling the students what is good practice by being specific about the feedback.
    5. “Read the problem silently and after 3 minutes, talk to your neighbor on how you did it.” Also, Why are these two right? Check with your neighbor. Talk it out” —> ‘Turn and talk’ — a good strategy.

    Papert said something similar to what Elliot said. “If the role of the computer is so slight that the rest can be kept constant, it will also be too slight for much to come of it.”

    This is my preferred stance and I crave the day when it comes. And I will continue to work hard towards it.

    In the meantime, I will look for the ‘good’ inside hard working teachers and students, meet them where they are, and encourage and support them to shift to the classrooms that you and I likely envision.

    I know Seymour would be extremely critical of this scenario. I think Elliot would be more in agreement with my position. He’d sure love that they were using handhelds! :-) Right Elliot!?

    • larrycuban

      Peter,
      Many thanks for your comment on the math lesson and your commitments. I appreciated the candor and pragmatic view of the math teacher I observed.

  9. This is a phenomenal discussion. I wonder how this community feels about the latest version of ExitTicket that was released today.

    http://exitticket.org

  10. Pingback: Obstacles and Solutions to Integrating Technology | Joe Bodnar: EDTECH Learning Log

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