“I’m not good at math. I failed it once.” We’ve all heard that, but here is something we never hear: “I’m not good at video games. I tried it once and I died on level one.” When a student fails in a video game, it is engaging. He or she says, “That was cool. I’m going to start again.”
But that’s not what we hear in a math class. This tells us that there is something radically different about how video games are designed and how our math textbooks and our state standards are designed. And it all comes down to three factors:
Compare that to the typical textbook layout. On the left page are a few examples, and on the right page are practice problems followed by word problems. Our state standards mandate that the problems in that lesson are at grade level, but are our students? If we teach directly from the textbook examples, any students who are not at grade level are already lost. It would be like starting a video game at level 28.
And do the practice problems build incrementally like the levels in a video game? Does problem 1 provide you with the skills to tackle problem 2? There’s a chance that the problems in the practice set were created randomly by computer software. Imagine if the levels in a video game were randomly sequenced.
Also, the student may not see math in a real-world context until those word problems at the end, and they may not know how they did until they get their homework back the next day.
We need to model our mathematics lessons after the design of video games: intentional and incremental development with quick feedback. For example, if we want to show why subtracting a negative is the same as addition, we can ask students to complete the patterns of problems below:
3–3=0
3–2=1
3–1=2
This starts simply. It is level one. All the students who can subtract one-digit numbers are on board. But what comes next?
3–3=0
As the subtracted number is lowered by one, the difference increases by one. And then what would we write?
3––1=4
But wait, it’s also true that 3+1=4. Therefore, the two negatives make a positive. Notice that we started simply and built incrementally in an intentional way. The simplicity of the first few problems gave the students feedback as they worked.
Here is another example. This is how I help my middle school students practice operations with integers. I give them the two numbers on the sides of the X in Example 1and ask them to find the upper number and lower number. In this case, the upper number is 12 and the lower is 7. Because I begin with such a simple example, all of my students realize that the upper number is the product of the side terms and the lower number is the sum. Then we can begin to “level up.”
Once they understand how the puzzles work, I can introduce examples that have integers as in Example 2.
Now they are practicing multiplying and adding integers, which was my goal. Later, we level up again by giving them the top and side numbers as shown in Example 3 Now they must divide and add.
And then I give them the bottom and side numbers in Example 4, so they have to subtract and multiply.
They have practiced working with integers in all four operations. And finally, we meet the beast at the highest level shown in Example 5.
Here, the side numbers are 9 and –4. The student has truly leveled up as this puzzle is more demanding cognitively. Students approach these puzzles like levels in a video game. The brain likes to have moderate and sequential challenges like they see when gaming or doing lessons like this.
Notice that I’ve intentionally sequenced these problems to intentionally bring the student to this level. If this is an assignment, I provide an answer bank, so the student gets the critical immediate feedback.
And what is my intention with this lesson? First, it provides critical ongoing practice in all four operations with integers. More importantly, it provides an incremental lead-in to factoring quadratics. If we want to factor x2 +5x–36. We can use the previous puzzle. The solution, 9 and –4, are the solution:
x2 +5x–36=(x+9)(x–4)
Teaching math with intentional and incremental development coupled with ongoing feedback mimics how our students’ brains interact with the video games that so engage them. Our textbooks then become a resource much like the dictionary in a language arts class. It has practice sets and sample solutions, but it is not an instructional tool. The greatest instructional resource in the classroom is the teacher presenting intentional and incremental instruction.
For more examples like these, explore some of over 100 activities in my TeachersPayTeachers store like the ones below.
But that’s not what we hear in a math class. This tells us that there is something radically different about how video games are designed and how our math textbooks and our state standards are designed. And it all comes down to three factors:
- Intentionality
- Incremental development
- Ongoing feedback
Compare that to the typical textbook layout. On the left page are a few examples, and on the right page are practice problems followed by word problems. Our state standards mandate that the problems in that lesson are at grade level, but are our students? If we teach directly from the textbook examples, any students who are not at grade level are already lost. It would be like starting a video game at level 28.
And do the practice problems build incrementally like the levels in a video game? Does problem 1 provide you with the skills to tackle problem 2? There’s a chance that the problems in the practice set were created randomly by computer software. Imagine if the levels in a video game were randomly sequenced.
Also, the student may not see math in a real-world context until those word problems at the end, and they may not know how they did until they get their homework back the next day.
We need to model our mathematics lessons after the design of video games: intentional and incremental development with quick feedback. For example, if we want to show why subtracting a negative is the same as addition, we can ask students to complete the patterns of problems below:
3–3=0
3–2=1
3–1=2
This starts simply. It is level one. All the students who can subtract one-digit numbers are on board. But what comes next?
3–3=0
As the subtracted number is lowered by one, the difference increases by one. And then what would we write?
3––1=4
But wait, it’s also true that 3+1=4. Therefore, the two negatives make a positive. Notice that we started simply and built incrementally in an intentional way. The simplicity of the first few problems gave the students feedback as they worked.
Here is another example. This is how I help my middle school students practice operations with integers. I give them the two numbers on the sides of the X in Example 1and ask them to find the upper number and lower number. In this case, the upper number is 12 and the lower is 7. Because I begin with such a simple example, all of my students realize that the upper number is the product of the side terms and the lower number is the sum. Then we can begin to “level up.”
Once they understand how the puzzles work, I can introduce examples that have integers as in Example 2.
Now they are practicing multiplying and adding integers, which was my goal. Later, we level up again by giving them the top and side numbers as shown in Example 3 Now they must divide and add.
And then I give them the bottom and side numbers in Example 4, so they have to subtract and multiply.
They have practiced working with integers in all four operations. And finally, we meet the beast at the highest level shown in Example 5.
Here, the side numbers are 9 and –4. The student has truly leveled up as this puzzle is more demanding cognitively. Students approach these puzzles like levels in a video game. The brain likes to have moderate and sequential challenges like they see when gaming or doing lessons like this.
Notice that I’ve intentionally sequenced these problems to intentionally bring the student to this level. If this is an assignment, I provide an answer bank, so the student gets the critical immediate feedback.
And what is my intention with this lesson? First, it provides critical ongoing practice in all four operations with integers. More importantly, it provides an incremental lead-in to factoring quadratics. If we want to factor x2 +5x–36. We can use the previous puzzle. The solution, 9 and –4, are the solution:
x2 +5x–36=(x+9)(x–4)
Teaching math with intentional and incremental development coupled with ongoing feedback mimics how our students’ brains interact with the video games that so engage them. Our textbooks then become a resource much like the dictionary in a language arts class. It has practice sets and sample solutions, but it is not an instructional tool. The greatest instructional resource in the classroom is the teacher presenting intentional and incremental instruction.
For more examples like these, explore some of over 100 activities in my TeachersPayTeachers store like the ones below.
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