A few weeks back we covered part 1 of how to select the right progress measures for reading. Just like with reading, effective math intervention requires using the right combination of intervention and progress monitoring. This article will review the role of progress monitoring within a multi-tiered system of support (MTSS) and how to select a math progress monitoring measure.
Because this topic can often feel abstract, we will take a look at a case example at the very end.
The Benefit of Formative Assessment Measures for Mathematics
One of the major goals of an RTI/MTSS model is to improve student learning outcomes through the use of evidence-based instruction, assessment, and intervention (Brown-Chidsey & Bickford, 2016). Assessment plays a critical role in any RTI/MTSS model for mathematics and differs in some ways from the assessments that teachers may be accustomed to using within their classrooms.
When teaching mathematics, teachers may be most familiar with using skill-based, criterion-referenced, end-of-unit chapter tests to measure student mastery of specific learning objectives. While this type of assessment serves a variety of purposes (including summative evaluation of student learning) formative assessment that accompanies intervention is important for students who have difficulties in mathematics.
There are two primary types of formative assessments: general outcomes measures and mastery measures.
General Outcome Measures
When an assessment measures all of the skills covered over an entire school year it is referred to as a general outcome measures (GOM). GOMs are used for universal screening as well. When used for progress monitoring, these measures are helpful because they show if a student is improving the skills necessary to show grade-level proficiency.
GOMs work well when a student’s current skills are near to the grade-level goals but they might not be as useful when a student’s current skills are significantly below grade level. This is because the items on the assessment could include too many that the student does not yet have the prerequisite skills to complete accurately.
When a student’s student’s current skills are significantly below grade level, it might be better to use progress measures that include a narrow set of skills. Mastery measures (MM) are assessments that include the specific skill that the student is working on in the current intervention. This type of progress measure is particularly important for math because of the hierarchical nature of math skills.
As student’s progress in mathematical learning, what they learned before must be used as a foundation for new learning. For example, it is very difficult to understand fractions without having mastered the four basic operations. When a student’s intervention includes learning one very specific math skill (e.g., times tables), mastery measures can be the best types of progress measure to use.
Determining Which Skills Need to Be Taught
Because of the key role that progress monitoring plays in knowing if an intervention is working, it is essential that progress measures for math be appropriately selected for individual students. In many cases, the results of a universal screening assessment may provide adequate information to help guide an educator in selecting an appropriate progress monitoring measure for a given student. Other times, additional assessment may be necessary to help pinpoint specific areas in need of progress monitoring.
The best place to start the search for the most appropriate progress measure is to determine what skill(s) a student needs to be taught.
FastBridge Learning Math Progress Monitoring Measures
In order to know which math skills a student most needs to learn, the FastBridge Individual Skills Report is an excellent resource. This report details what skills a student needs to learn next. Once the area(s) most in need of targeted instruction is determined, a progress monitoring measure most closely aligned to the instructional focus should be selected. FastBridge offers a variety of math progress monitoring measures, which are summarized in the table below.
||Counting and Cardinality|
||Counting and Cardinality|
||Expressions and Equations|
||Number and Operations in Base 10|
||Expressions and Equations|
In some cases, a student might need to work on multiple math skills. When this is the case, it is important to provide intervention that focuses on the skill that most closely follows from what the student already knows.
A Case Study Example: Using FAST aMath
Alison is a third-grade student who participated in universal screening for mathematics skills. Her school uses FAST™ aMath to screen all students for broad math abilities, three times per year. Alison’s score on the fall administration of aMath was flagged as “high risk” for math difficulties because her score on aMath was below the 20th percentile.
The results of Alison’s universal screening assessment are indicative of her need for supplemental math instruction. However, with a more detailed analysis of Alison’s strengths and weaknesses, the math interventionist can determine the initial focus of the targeted intervention.
1. Selecting the Appropriate Skill Area
Alison’s aMath Individual Skills Report provides information about specific math skills that Alison has “mastered,” is currently “developing,” and will need to be taught in the “future.” These math skills are organized into the following six domains:
1. Numbers and Operations
2. Counting and Cardinality
3. Operations and Algebraic Thinking
4. Numbers and Operations in Base Ten
5. Measurement and Data
Below are Alison’s current math skills within the "Numbers and Operations in Base Ten" domain.
She currently has not mastered skills listed within the domain. However, several other developing skills are listed. The math interventionist examines the list of developing skills within this domain and considers the sequence in which early mathematics skills are taught. She then determines that “reading and writing numerals to 120” is one reasonable skill area she can begin targeted intervention.
2. Selecting an Appropriate Progress Measure
After selecting the skill area to target during the intervention, the math interventionist must select an appropriate progress measure.
After examining the progress monitoring measures, it's clear that earlyMath Numeral Identification – 1 is the closest match to the area being targeted for instruction. FastBridge suggests a mastery rate goal of 42 numerals identified per minute. Additionally, a weekly growth rate goal of .79 numerals identified correctly per minute per week is suggested as evidence of an effective intervention.
With this information, using earlyMath Numeral Identification – 1 as the progress monitoring tool, the teachers sets a goal of 42 numerals identified per minute. Additionally, a weekly growth rate of .79 numerals identified correctly per minute per week can be used as a basis to determine if Alison’s weekly growth rate is adequate and to determine if the intervention in place is meeting her instructional needs.
The math interventionist administers the progress monitoring assessment weekly and graphs Alison’s progress.
After analyzing the graph, the interventionalist can see that Alison’s current weekly growth rate is exceeding the weekly growth rate goal of .79 numerals identified correctly per minute per week. This suggests that the current intervention is meeting Alison’s instructional needs.
3. Selecting the Next Skill for Targeted Intervention
Alison will soon meet the goal of 42 numerals identified per minute on earlyMath Numeral Identification – 1. After that, the interventionalist can reexamine Alison’s aMath Individual Skill Report to identify a new area for targeted intervention (e.g., composing and decomposing from 11 to 19, addition within 100, place values for 1s, 10s, and 100s).
When the focus of targeted instruction is updated to a new skill, a new progress monitoring measure should be selected so that it is in alignment with the new instructional focus.
Progress monitoring plays an integral role within an RTI and MTSS framework. Progress monitoring tools are used to make week-to-week decisions about the effectiveness of a particular intervention or instructional delivery. In order for progress monitoring tools to serve this purpose, they must be carefully selected so that they are closely matched to the skill area(s) that are being targeted during mathematics intervention.
Brown-Chidsey, R. and Bickford, R. (2016). Practical handbook of multi-tiered systems of support: Building academic and behavioral success in schools. New York, NY: The Guilford Press.
Riccomini, P.J. and Witzel, B.S. (2010). Response to Intervention in Math. Thousand Oaks, CA: Corwin.