When first thinking about making a manipulative for this making for learning project, we both thought about what would be the most beneficial tool for the grades we were teaching. We had conversations about what we thought our students were struggling with the most, and we both came to the conclusion that our students needed to work on understanding place value. The project we made is designed to check for student understanding of place value and the value of each number. They will use cubes that have a number spinner, to keep track of the number in that place and blank cubes as place holders. Our manipulative is designed so they can be stacked on top of each other in order to see the number’s place value.
How is the user of your manipulative supposed to learn from working with your design? The user of our manipulative is supposed to learn place value while working with our design. They will be able to change the numbers on the spinner to represent the numbers 1-9. The manipulative will have blank cubes or zeros for the ones, tens, and hundreds place that aren’t being represented. The cubes will also be able to be stacked so that students can see the difference in each place. By having a tiered design students can see the whole number and write all the numbers down as they appear. With this design students can learn where a number’s place value is and how a number looks when they are separated in their perspective place values. We also believe that students should also see that the block with 0 have a place and a value. Using 0s in our design, will allow students to see that a 0 is a label as a placeholder, which will help them with base ten concepts. For example, the number 945 will look like 900, 40, and 5 with the blocks. They will learn that the 9 in the hundreds place is actually 900 and so on.
How does the design of your technology reflect your understanding of what mathematics is and of how learning happens?
The design of our technology reflects our understanding of what mathematics is and of how learning happens. With our design we will be addressing a common misconception that students first make when they are learning about place value. Most students don’t realize the value of each number in a multi-digit whole number. For instance, it is difficult for students when they are first learning about two and three digit numbers to realise not only place value, but what each number represents. For example, as a first grader tries to learn numbers greater than 10, they may struggle with the understanding that the number 32 is 3 tens and 2 ones, or 30 and 2. With our manipulative the students will be able to see up to the thousands place the value of each number in a number with more than one digit.
What would it mean for your project to be successful in terms of learning?
In order for our project to be successful in terms of learning the students will need to be able to successfully write the whole number with the place value blocks and be able to identify the value of each number in expanded form. For example, if we were to ask a student to make the number 1,638 with the cubes they will be able to take the ones cube and turn it to 8.Then place a tens cubes underneath and turn it to 30. They will continue to take the hundreds cubes and turn is to 600, and finally under the hundreds cube, place the thousands cube with the spinner turned to 1,000. After placing all these numbers in the correct spot they will be able to write down 1,638 underneath. In order for it to be wholly successful, the student should then be able to state the value of a number within the whole number. If we were to ask what is the value of the 3 is in 1,638, they should be able to answer with the value 30.
What would it mean if it were to fail to work?
If our manipulative failed to work, it would mean several things. The first thing is that our manipulative failed to help the student understand which numbers are in the ones, tens, hundreds, or thousands place. Either because our cubes were too confusing or they were not labeled correctly. Another way it might fail to work is if the student does not understand how to write the whole numbers down after stacking the cubes correctly. In addition if the teacher’s explanation of the manipulative isn’t clear then our students would definitely fail their tasks. Another way that our manipulative might fail to work is if the student is still unable to identify the value of any given number within a whole number. For example, if we gave them the number 463 and the student is asked what is the value of 6 and they are unable to answer 60 or 6 tens, then our manipulative might have failed.
What kind of testing could you imagine carrying out for your design?
We believe the best type of testing for this design would be to sit with a student one on one and recite a number that they can build with the manipulative. Hopefully with success the student would be able build any number using the ones, tens, hundreds, or thousands cubes. The student will then be able to verbally tell us the value of any number when asked. This can be done several times with several different numbers of different values. To push our manipulative even further than just place value it can also be used to create two numbers and add them together. When a number has to get carried over they will be able to actually see how that number turns into the value of the number to the left. For example when adding 97 + 84. They can see that the 1 from the 11 would turn into a 10 and then the 1 from the 10 would turn into a hundred. There are many possibilities for the use of our manipulative, but our end goal is that students walk away knowing that success with place value is possible.