By: Rachel Brown, Ph.D., NCSP
In fall 2016, FastBridge Learning released additional math assessment tools in FAST™. The new and revised measures include:
- CBMmath: Concepts and Applications (new)
- CBMmath: Process (revised scoring)
These additional math tools were created in response to user requests for math assessments that are easier to score and aligned to state standards. Both of these new math tools are in Lab phase during the 2016–17 school year. This means that they are available for FAST™ users but require additional data analysis and user feedback before they will be recommended as part of a multi-tier system of support (MTSS).
CBMmath: Concepts and Applications (Lab)
CBMmath Concepts and Applications (CBMmath CAP) is an additional form of curriculum-based measurement (CBM) for mathematics. Like other CBM tools in FAST™, CBMmath CAP is designed to show a student’s current skills in relation to year-long learning goals. CBMmath CAP is a computer-based assessment of applied math that includes items spanning computation fact fluency to multi-step algebra problems. Instead of grade levels, there are skill levels from 0 through 8. CBMmath CAP items were developed from an existing bank of FAST™ math items, including those in aMath and Standards-Based Math Assessments. The items were all developed in accordance with the mathematics learning hierarchy in the Common Core State Standards, including Counting and Cardinality, Operations and Algebraic Thinking, Number and Operations in Base 10, Number and Operations, Measurement and Data, and Geometry.
Procedure. CBMmath CAP is a timed measure that is computer administered and computer scored. The times allotted for CBMmath CAP vary according to grade levels as follows.
- Screening times by level:
- K-3: 15 minutes
- 4-5: 20 minutes
- 6-8: 30 minutes
- 9-12: 30 minutes
- Progress monitoring times by level:
- K-5: 15 minutes
- 6-8: 20 minutes
- 9-12: 20 minutes (expected availability 11/21/16)
Students complete about 20 math problems by selecting one of four answer choices. Each possible answer can be read aloud by clicking on a picture of headphones next to each answer choice. Students can also have each question re-read by clicking on a headphone picture.
Scores and Uses. CBMmath CAP reports the number of problems that a student got correct in 10 minutes. When a student takes shorter or longer than 10 minutes to complete a CBMmath CAP session, the score will be prorated to match a 10 minute interval. CBMmath CAP can be used for both universal screening and for progress monitoring. When used for fall screening, FAST™ recommends that students complete the level below the current grade. This is because the items in each level reflect content that might not yet been taught. For winter and spring screening, students complete the level matching their current grade. When used for progress monitoring, FAST™ recommends the level matching the student’s current grade unless the student is three or more years behind grade level in his or her math skills.
Another enhancement for FAST™ users is the revised scoring available for CBMmath: Process. The CBMmath Process assessment has been part of the FAST™ math suite for several years, however, many teachers sent feedback that it was very cumbersome to score. The CBMmath Process assessment is the only FAST™ measure that must be administered and scored from paper-and-pencil. Specifically, in its original version, after the students completed the CBMmath Process assessment, the teacher would use an online scoring key to analyze each individual step and process that the student used to solve the problems. This scoring method, a form of error analysis, can be very helpful for teachers who want to learn about the details of an individual student’s math difficulties. Still, using an error analysis scoring method for all students could be more time-consuming than needed because many students will make few mistakes, and their work does not require such in-depth analysis.
Rapid Scoring. Based on the above feedback from teachers, FastBridge Learning convened a panel of CBMmath Process users, content experts and researchers during the summer of 2016 to design a revised alternative scoring method. The panel developed a new, additional, scoring option for CBMmath Process. This new method is called “Rapid Scoring” and involves evaluating each student response in relation to three color-coded score options:
- Green = 100% points
- Yellow = 50% points
- Red = 0 points
To assist teachers with using this new rapid scoring option, the “rules” for awarding points are as follows:
- 0 errors = 100% (green)
- 1-2 minor errors = 50% (yellow)
- More than 2 errors = 0 points (red)
100% of points are given when there are zero errors, 50% of points when there are two or fewer minor errors, and no points when the student makes more than two errors.
Error Analysis. Although the new rapid scoring method offers a faster way to score the CBMmath Process assessment, it has the limitation of less detailed information about a student’s math problem solving process. For this reason, the original CBMmath Process scoring method has been retained and is now known as the “Error Analysis” method. This method entails coding each student’s answers using error types. Here is a list of possible error types:
To use the error analysis scoring method, the teacher opens the error analysis scoring option and clicks on each problem on which the student made an error. Note that this method requires coding only errors, and the default score value will be all the points unless the teacher codes an error. To enter an error code, the teacher clicks on the problem with the mistake and then on the corresponding error code from the list on the screen. For example, in the sample below the student made mistakes on problems 1 and 7.
If the student’s answer to the first problem was 140 instead of 0, the teacher would mark both a Calculation-Multiplication (Cx) error as well as a Primary Operation (PO) error. This is because the student not only did not multiply correctly, but also gave an entirely wrong answer and appears to have done the wrong operation. Similarly, on problem 7, if the student’s answer was 427, the problem would be marked with both a Calculation-Multiplication (Cx) error and Calculation-Addition (C+) error because of errors in the initial multiplication as well as in adding the values correctly.
Scores and Uses. The Rapid Scoring method was added with the idea that it would be most useful for universal screening of math process skills. Similarly, the Error Analysis scoring method was retained with the idea that it would be most helpful for teachers during progress monitoring of students’ math skills. Detailed guidance about how to administer and score both the Rapid and Error Analysis methods is found in the FAST™ Knowledge Base (FAST™ log in required).
Together, the addition of the CBMmath CAP and revised scoring procedures for CBMmath Process provide teachers with additional tools for identifying and monitoring students’ math skill acquisition. These two new tools remain in Lab phase for the 2016–17 school year, and FAST™ users are encouraged to send feedback for further future refinement to firstname.lastname@example.org.
Dr. Rachel Brown is FastBridge Learning’s Senior Academic Officer. She previously served as Associate Professor of Educational Psychology at the University of Southern Maine. Her research focuses on effective academic assessment and intervention, including multi-tier systems of support, and she has authored several books on Response to Intervention and MTSS.