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With the pressure to ensure all students learn the assigned curriculum, test well, and stay healthy, it can be hard to effectively teach the whole child. We’ve asked some math education experts to answer questions about how to teach the whole child during middle school math.
- Is it appropriate to allow students to help out so they feel good about themselves?
- Can using games as a reward backfire?
- Why can’t students use calculators for all of their work?
- How can I help my students see that they can’t always do mental math?
- Coach’s Corner: How can I help my math teachers balance the aspects of their job?
“I have a student who always asks if I need any help with anything in class. She does very well and usually finishes her work early. Helping out seems very important to her. What kinds of things could I ask her to do that would make sense in a math class? Would asking her to help be appropriate, or should I have her work on some more challenging math instead?”
Mike Delasandro, veteran middle school math teacher in Princeton Junction, NJ, has encountered several students like these over the years. He shared, “One successful thing I’ve done is to ask them to make an answer key for a particular assignment that the other students could use to check their work. This helps your student practice math skills while also helping you and the other students. I also like to give students a variety of assignments to choose from to meet their needs.”
Linda Scanlan, an expert math coach also in Princeton Junction, NJ, urges us to be cognizant of students’ personal needs. She says, “Some students (and people) have a need to help, it makes them feel valued. A small classroom job such as ‘material manager’ can make students feel needed and included. Offer these types of small jobs to not only this student but other students as well, perhaps on a rotating basis.”
“As part of our math program, we have some really good math games on our computers. I will sometimes tell my class that when they finish their assignments, they can choose to work on the math games. Now I have kids racing to finish and making careless errors just so they can get to the games. I’ve reminded them that the assigned work has to be done well, but they are still rushing. Is this incentive a bad idea? What would you recommend I do?”
Linda Scanlan recommends first considering the purpose of these games. “Offering educational games is not a bad idea nor a bad incentive, but it may need to be structured differently. We do not want to send a message that if you rush through the work, you get rewarded with a game or that when you work carefully and slowly you are punished by not getting a chance to play the game. If the game is educational and valuable, then all students should have the opportunity to play.”
David Hatfield, a lead learning scientist with McGraw Hill, mentions some important considerations when using these games as incentives. He says, “It’s great that you have game-based learning options available and that your students are responding so well to game-based activities. While the incentive approach is understandable, setting up access to the game-based activities strictly after finishing other assignments does create competition between the two. One option might be to try to integrate the game-based activities earlier into your lessons. Do they offer examples of particular objectives you’re focusing on? If so, maybe having students experience them first playfully might provide an interesting context to link to instructionally.”
“I have a student who wants to use a calculator for any of the computation we do in class. He said that’s how people in the real world do it, like engineers and scientists, so why shouldn’t he? I have some ideas of my own on how to answer this, but I’d be interested to hear from others.”
Looking at the big picture in middle school math, Mike Delasandro says, “For most basic arithmetic lessons, a calculator is not appropriate because students are learning about number sense and operations. For higher level math and problem solving, when the arithmetic is not the primary objective, using a calculator can be a valuable and time-saving tool. I would probably tell that student that he is correct—engineers and scientists do use calculators. However, they understand what the calculator is doing, because they learned the concepts first.”
Margaret Bowman, a math academic designer with McGraw Hill, likes this student’s thinking but suggests helping him develop a little more perspective. She says, “It’s true, people in the real world do use calculators. However, successful scientists and engineers also have years of experience building the foundational math skills he’s working to build right now. I would build on his assertion about real-world application to help him understand the need to work without calculators. How do scientists and engineers know what computations they need to complete in order to solve a problem? Or, how do they know what questions to ask in order to get the answers they need? Furthermore, how do they interpret the answer a calculator provides, or recognize if an answer doesn’t make sense and perhaps they made an error when entering information into the calculator? They have the foundational skills about math concepts that he’s building every day.”
“My best math student insists on using mental math for all of his calculations. He’s very good at it and never writes anything down. He is very proud of this too. The rest of my class is now trying to do the same thing, as they all look up to him, but they are not capable of doing it. How do I handle this situation?”
Linda Scanlan suggests considering other kinds of assignments and not to forget the importance of estimation. “Some students are very good at mental math. Some students are not. First, we should celebrate our differences. Second, you might try asking questions in a way that can’t be done mentally or have more than one correct answer. Estimation is an important skill in math. Asking for an estimate first and explaining the reason for the estimate will develop other skills beyond mental math. Go a little further and ask them why is it just right, and to justify their answer.”
David Hatfield recommends helping students like this get involved in sensemaking and multiple modes of expression important in this situation. “One approach that may benefit your class and challenge your high-performing student is a focus on mathematical discourse and sensemaking. For example, you might work in opportunities for all of your students to talk about how they work through math problems as a whole class or in a pair-share context. You might even set a challenge to use multiple modes–including speaking, drawing, and whatever creative element they choose to show their solutions! While mental math is, of course, a wonderful skill, expressing mathematical thinking can be so much richer.”
“Teachers I coach have curriculum demands, standards to meet, assessments to give and analyze, and parents to deal with. How do I help them strike a balance between all this and their personal experience in deciding what an individual student needs?”
Margaret Bowman says this might be the time to look to how technology can support your efforts. She says, “Truthfully, there is no easy answer to this question. The average teacher’s workflow is overwhelming and difficult for teachers to keep pace with classroom demands. Your teachers are not alone in this balancing act. As a coach or lead teacher, I would argue that your most important role is to help them preserve that uniqueness and creative energy so that they can continue to inspire and connect with students! The art that they bring to their profession can’t be replaced or replicated. But in order to make that possible, while meeting all the demands you referenced, there has to be an element of technology to close the gap. The technology your teachers use should minimize the complexities in their workflow—it should help them collect information about student learning, identify gaps, and address student needs. It should, of course, be used purposefully—because when technology isn’t used purposefully, it has a tendency to actually disrupt and complicate teachers’ workflow!”
Linda Scanlan urges collaboration among teachers as well as a classroom culture dynamic. She answers, “Teaching can be overwhelming no matter how many years of experience the teacher has. The demands are great, and meeting the students’ needs should be the number one priority. Each teacher needs to teach math in a way that tells a story—a story that they believe in and a story the students buy into. Talking to students, knowing them personally, and involving them in decisions helps teachers meet students’ needs. Encouraging teachers to collaborate, plan together, share materials, observe each other, and lean on each other for support will develop teacher collective efficacy.”
Want more math expert advice? Check out Ask the Experts: Assessment in Middle School Math and Ask the Experts: Differentiation in Middle School Math
Illustration: Jennifer Jamieson
