The learning tool we have re-created is a number line that helps children solve addition and subtraction problems up to the number 20 without using paper and pencil. The number line would be blue with black numbers 1-20. Then, we would create two separate points so the student is able to jump forward and back. Green would represent addition and red would represent subtraction. The advantage of using this number line is to show a tool for helping children develop mental arithmetic with smaller numbers. Our grade level would focus on 1st grade. We decided to use two points so that the student wouldn’t get confused. The green point would move from left to right where as the red point would move right to left. We were thinking in terms of how the number line is written out ,we count forward towards 20 for addition and when we subtract we count backwards towards 1.
When beginning to learn adding and subtraction children may use the number line to find the answers before they can do it automatically in their heads. For example, the answer to the subtraction problem 18-5; equals 13. Once a student sees this visually it very well can help with math concepts. They are made aware of the difference between these two numbers by looking on the number line. It can start to make sense for these young learners. Many students need concrete examples of how to solve problems in mathematics. As stated in our book, many students will use counters, bar diagrams, or number lines(models) to solve story problems. The model is a thinking tool that helps them both understand what is happening in the problem and means for keeping track of the numbers and steps in solving the problem. Van de Walle et al. (2014).
Teachers use many forms of technology to teach students. For example, smart boards, tablets and computers. Technology is becoming more prominent in today’s classrooms. In mathematics, these tools can be very useful for teachers in engaging students to new material and lessons. Using technology to get students engaged in a mathematical lessons can be done with the use of our number line, which is a form of technology. We consider this to be a concrete manipulative that reinforces a mathematical concept of number sense.
The number line can be overlooked in many classrooms, applying it with technology can make it more appealing for these young learners. The number line can be a very effective tool for memorizing and practicing counting with numbers. When a student can visually watch the jumps forward or backwards representing adding and subtracting, number operations can make sense. Children appeal to things that are bright and colorful, we hope they will be more inclined to focus on our tool because it’s not monotone or as blain as paper and pencil.
We think one of the indicators that our class is learning is if they are getting an equation, 4 + 3 and knowing they can start from 4 on the number line. They would continue by adding 3 to get an answer of 7. Sometimes children will start on their fingers counting to 4 and then adding 3 more. The number line is a tool to facilitate adding and subtracting. Eventually the children could have a mental image of the number line and be able to automatically add or subtract numbers to 20. Some ways we will implement support is: Avoid revealing whether the student’s answer is right or wrong, let students share their thinking freely without interruption and ask students to demonstrate their understanding in multiple ways. Van de Walle et al. (2014)
One way to assure that our number line is effective and productive we would have to use a rubric that shows the students understanding of this tool is working. “A rubric consists of a scale based on predetermined criteria with two important functions to see what is central to excellent performance, and (2) it provides the teacher with scoring guidelines that support analysis of students’ work.” Van de Walle et al. (2014). For example, the students need to be able to use logical reasoning, expressed a grasp of numerical relationships and structure and solve the problems accurately and effectively.
As opposed to asking what it would mean if the manipulative were to fail. I think a better question could be finding out the cause of why it didn’t work. Experimenting from the beginning steps where it went wrong might be a good place to start. We would have to consider if the design is not simple enough for a first grader to understand the concept of this number line. Were we able to explain it in a way that was not to complex and with minimal simple steps. Is the design over whelming at first sight, which is not what the design is supposed to do. This design should be simple in the since that it has clearly identified parts. The number line is blue with large enough numbers that are identified. The moving parts are simple as well, Green represents addition and Red represents subtraction. The number line is to work the same ways as if done with paper but things are in color so the student can clearly identify what strategy they are conducting when using the number line.
To test the number line, we would start off with simple problems: 6+1=7 or 5+3=8. Explain to the students that when adding we count from left to right on the number line. The green point is what represents addition. So if that counter is not moving left to right, their answer will not be correct. Simple examples of subtraction would be: 5-3=2 or 10-4=6. When subtracting the points move from right to left on the number line. The red point represent subtraction so if the counter does not move from left to right then its not subtraction. For examples of complex addition and subtraction problems to solve:
Problem 1: 8+ __= 20
We have to start at eight and end at 20. How many jumps do we need to get to 20? We would do the jumps in green. We will do the first examples as a class, then they will work individually to get the answer : 12 jumps.
Problem 2: 20 -__=15 We will model starting at 20. Asking How many jumps do we have to make backwards to get to 15? We will do this in red. The answer is 15.
Perhaps the design just needs a tweaking from the original concept. It is possible observing the children’s’ strategies to uncover their thinking which we can realize why it failed to work or possibilities of what needs to change. It would be important to ask the set group of students why it didn’t work for them and most importantly ponder on their answers.
In summation, if all these approaches failed, we would move on to a different tool to help further the classes’ understanding of addition and subtraction. Ultimately, we must create a tool that supports the learners’ conceptual understanding of how adding and subtracting works.
Van de Walle, John A. Teaching Student-Centered Mathematics. Developmentally Appropriate Instruction for Grades 3-5. Boston:Pearson, 2014