Guiding Student Learning
Ongoing math assessment is one of the key principles in understanding your students’ mathematical thinking. To make learning meaningful, you must first have a thorough understanding of what prior knowledge your student has.
Below you will find a series of basic addition problems that you can use as an assessment test for math skills. These problems cover basic joining concepts and progress through the identified continuum of knowledge development as detailed in the findings of Fennema, Carpenter, et al., and will give you a better understanding of where each student falls on that continuum. These problems are provided as a math assessment for addition problems using CGI math, but may be used as a math assessment for any curriculum program. From there, you may develop your goals for instruction.
Please refer back to earlier articles in the series to understand what the notations mean after each problem.
1. Mary had 6 pieces of gum. Beth gave Mary 6 more pieces of gum. Now how many pieces of gum does Mary have? (Join-Result Unknown 1)
2. Mailman Mike had 6 letters to deliver. His friend, Mailman Larry, gave Mike 22 more letters to deliver. Now how many letters does Mailman Mike have to deliver? (Join-Result Unknown 2)
3. There were 51 geese on the soccer field. 28 more geese landed on the field. Now how many geese are on the soccer field? (Join-Result Unknown 3)
4. Megan has 59 suckers. Her mom gives her 23 more suckers as a treat. Now how many suckers does Megan have? (Join-Result Unknown 4 with regrouping)
5. I have 37 pieces of gum. Mrs. Fricano gives me 23 more pieces of gum. Now how many pieces of gum do I have? (Join-Result Unknown 5 with zero as a place holder)
6. Jane has six brown sheets of drawing paper and four yellow sheets of drawing paper. How many pieces of drawing paper does she have? (Part-Part-Whole, Whole Unknown)
Solution Strategies and a Sample Problem
You can use this assessment test for math to track your students’ progress over time as they develop their mathematical thinking skills. Here is a sample Joining problem:
Sara has 2 markers. Her mother gives her 6 more. How many markers does Sara have now?
Children’s solution strategies evolve over time. At the most basic level, children use physical objects (like counters or their fingers) to directly model the action described in the problem. For Joining problems, this strategy would include joining all of the parts in the problem to discover the total number. Using the sample problem above, the student might put 2 markers in one pile, 6 markers in a different pile, and then count all of the markers to find the answer.
Over time, their solution strategies become more abstract and efficient. As a child’s mathematical understanding progresses, the direct modeling is replaced by Counting Strategies. This will include counting on from the first number (2…3,4,5,6,7,8) and later, counting on from the larger number (6…7,8) - which is typically more efficient.
At the final stage of understanding, students will use known number facts to solve a problem. (6+2=8)
Other Problem Types
This addition assessment test for math skills can also be adapted for use with other problem types. This includes problems involving subtraction, multiplication, division.
- The information offered in this article is based on the author’s extensive experience using CGI in the classroom
This post is part of the series: Math Assessment Test - Creating Baseline Data to Guide Instruction
This series of articles will give specific problems which can be used to create a math assessment test for addition, subtraction, multiplication and division concepts. The math assessment test results can then be used to guide instruction for students on an individual basis.