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Selecting Math Progress Measures

By: Rachel Brown, Ph.D., NCSP

The FastBridge Learning system has many math assessments that teachers can use to monitor student progress. In order for such monitoring to be effective the progress measure must match the skill that the student is learning in the selected intervention. FastBridge math progress measures include tools that evaluate students’ mastery of math fact fluency, applied problem solving, and the processes that students use to solve problems. This blog will review the available measures and how to select the best progress measure to match each student’s instructional level.

Available Measures

The following table provides a summary of the available math progress measures, the levels available, and skills covered.

Measure Levels Skills Covered
earlyMath K-1 All essential pre-mathematics and early mathematics skills, including numeral identification, number sequences
CBMmath Automaticity 1-3 Fact fluency with addition, subtraction, multiplication, and divisions with two forms

  • General Outcome Measures (mixed skills)
  • Single Skill Mastery (single skills)
CBMmath Concepts and Applications (CAP) K-8 Application of fact fluency to different problem types with two forms

  • General Outcome Measures (mixed skills)
  • Single Skill Mastery (single skills)
CBMmath Process 2-6 Processes used to solve multi-step problems with two forms:

  • General Outcome Measures (mixed skills)
  • Single Skill Mastery (single skills)

Notice that the measures are organized by skill levels, not grade levels. This is because the FastBridge assessments are designed to track student progress toward specific math skills and not grade level equivalents. Grade level indicators are arbitrary designations but do not necessarily define what skills a student has mastered. FastBridge skill levels indicate a continuum of specific math skills from level K through 8. Another important feature of FastBridge math progress measures is that they include both general outcome measures (GOM) and single skill measures (SSM).

General Outcome Measures (GOM) are assessments that include a combination of problems reflecting the skill level. For example, a GOM for level 3 will include addition, subtraction, and multiplication problems as well as problems with different numbers of digits in each part of the problem (e.g., 3 digit by 2 digit, etc.). Mixed skill GOMs provide a way for teachers to learn how well students can switch between problems requiring different operations and skills. GOMs are the type used for universal screening, but can also be used for progress monitoring when a teacher would like to know if a student can switch between problem types.

Single Skill Measures (SSM) include problems of all one type. For example, a level 1 automaticity SSM probe might include all addition facts to 18. SSM are used for progress monitoring only and provide a way for teachers to know if a student has mastered a specific skill being taught. Once mastered, both the instruction and progress measure are then adjusted to the next skill.

Selecting a Math Progress Measure

The first step in selecting the best progress measure is to know what skill(s) a student needs to learn. The best way to identify students’ instructional needs is to conduct universal screening with a FastBridge Learning screening assessment. The screening assessment will show all students’ current math skill levels as well as which students have or have not met benchmark learning goals. In the FastBridge system, indicators of risk in relation to benchmarks are exclamation marks. Students whose score indicates some risk of not reaching the end of year learning goal are indicated with one exclamation mark (!) and those at high risk are indicated with two marks (!!). These indicators are designed to help teachers know which students might benefit from additional instruction or intervention. All screening scores should be compared to other sources of information about a student’s current skills in order to validate score accuracy.

Although the screening scores provide a first level of information about student math performance, they do not indicate each student’s current instructional needs. FastBridge Learning offers several reports that teachers can use to see what skills a student has mastered and what ones still need to be learned. Helpful reports for identifying specific skill needs are:

Report Name Screening Measure(s) Available Information Included
Individual Skills aMath (screening only)

 

earlyMath Composite

CBMmath Automaticity

CBMmath CAP

CBMmath Process

Student-specific listing of which math skills a student has mastered, are developing, or are in the future

 

Tables showing which specific items a student got right and wrong

Group Skills earlyMath Composite

CBMmath Automaticity

CBMmath CAP

CBMmath Process

Class-wide summary of what skills were weaker or stronger for the entire class

Sample Individual Skills Report:

The above sample shows the top of the aMath individual skills screening report for a third grader. This student is at high risk for math difficulties. In order to know what skills this student need to learn, and what progress measure to use, examine the skill set sections that are below the above summary. Here is the Number and Operations in Base 10 skills summary for this student:

This student does not yet have any mastered skills in this area. When reviewing the Individual Skills report, teachers are encouraged to look closely at the developing skills section. These are the skills that a student needs to master next before going on to more advanced future skills. When a student’s list of developing skills is long, the teacher must select which one will be included in the current intervention. This selection should take into account several factors, including what skills are the focus of current classroom instruction and what skills are most essential for overall math development. In this case, the student needs to master knowing and writing numerals to 120 and that is a very basic skill. Intervention should focus on this skill and Numeral Identification-1 would be the best progress measure to use.

The Individual Skills reports for earlyMath and the CBMmath assessments are different than for aMath. These reports show the actual items that the student got right and wrong on each part of the assessment. Here is an example for Numeral Identification completed by a Kindergarten student.

The above report format shows the teacher exactly which numbers the student does or does not know. In this case, Numeral Identification would again be the recommended progress measure.

Sample Group Skills Report

The Group Skills report is available for earlyMath and the three CBMmath assessments. This report provides a breakdown of how each student in a class did on each subtest in the earlyMath Composite.

The Group Skills report is organized to show overall class performance on the skills covered in the selected assessment. The above example shows part of a Kindergarten class performance on Numeral Identification. In this class, there were three numerals that less than 80% of the students knew (e.g., 28, 29, 31) This feature is designed to help teachers know what additional whole group instruction would benefit all students. When 80% or more students in a class have mastered a specific skill, it does not need to be taught at the whole class level, but certain students might need small group or individual instruction to master the skill. When fewer than 80% of students in a class have mastered a skill, ongoing whole class instruction of that skill is recommended. The above example also shows which students need additional instruction on some numerals. Students should attain at least 90% accuracy on a numeral to considered it mastered.

Instructional Hierarchy

All FastBridge Learning math progress measures reflect a skills hierarchy such that beginning skills are included at the lower levels and more advanced skills at the higher levels. This is done because certain basic math skills must be mastered in order for students to move on to math proficiency. The skills hierarchy included in FastBridge Learning assessments comes from two main sources: (a) National Council of Teachers of Mathematics (NCTM), and (b) Common Core State Standards (CCSS). The NCTM first published an instructional hierarchy and guidelines for math instruction in 1989. More recently, the CCSS were published by the National Governor’s Association to provide states and school districts with more uniform learning targets at each grade level. There are many similarities between these guidelines, including an emphasis on student mastery of all basic math facts across the four basic operations (i.e., addition, subtraction, multiplication, and division). Importantly, students need to achieve automaticity with math facts so that they can use them while completing other math problems. Such automaticity was identified as a cornerstone skill for later math proficiency in the 2008 National Math Advisory Panel Report (NMAP). Once students have mastered basic facts, they are ready to use these facts to solve other types of math problems, including multi-step and story problems as well as solving for a variable.

Matching Skills to Progress Measures

The skill hierarchies reflected in the NCTM and CCSS guidelines, and emphasized in the NMAP, are the basis for how the FastBridge Learning math progress measures are organized. The following table shows the skills and which FastBridge Learning math assessments can be used for progress monitoring in those skills.

Skills Example Measure(s)
Numbers and Operations Use fractions on a number line CBMmath CAP
Counting and Cardinality Count to 100 by 1s and 10s earlyMath Number Sequence
Operations and Algebraic Thinking Addition with objects and pictures CBMmath Automaticity
Number and Operations in Base 10 Place values for 1s, 10s, 100s CBMmath Process
Measurement and Data Measure with standard units CBMmath CAP
Geometry Names of basic shapes CBMmath CAP

Once a student’s specific math skill instruction need has been identified, teachers can select the appropriate progress measure from the Table above. The skills are listed from easier to more difficult. In the early primary grades (e.g., K and 1) the instructional focus is usually on learning numerals, the quantities they represent and base 10 place value. The best FastBridge Learning progress measures for these skills are earlyMath Numeral Identification and earlyMath Number Sequence-1. Note that these measures do not have separate GOM or SSM but only one form because these are distinct skills.

With these skills, students can move on to learning the single digit (or up to 12) math facts for addition, subtraction, multiplication, and division. Automaticity of math facts is essential for later math proficiency because such automaticity will determine how quickly a student can recall and use these facts to solve more complex math problems. When a student does not have the basic operation facts memorized, trying to complete more difficult problems will be frustrating or impossible. The best progress measure for students working toward fact fluency is CBMmath Automaticity. This measure has both GOM and SSM and the specific form to use depends on what skill the student needs to learn next. Usually, a SSM is best for progress monitoring automaticity. It is important when using CBMmath Automaticity to review the student data often and have the student move up to the next skill once each one is mastered. Although schools might have local criteria for mastery, a general guideline is for the student to reach the low risk benchmark score within the time limit. Although it consists of only 3 levels, CBMmath Automaticity can be used with students in the upper elementary, middle, and high school grades who have not yet mastered all basic math facts.

After students have developed automaticity with basic facts, they can be monitored with either CBMmath CAP or CBMmath Process. The decision of which to use should reflect the local curriculum and learning goals. CBMmath CAP reflects a wider range of applied math skills that require using basic facts to solve applied problems. CBMmath CAP includes content matched to the skill hierarchies in most U.S. published math programs and has GOM and SSM forms. For students with specific skill problems, such as those involving fractions, the SSM is the best choice. For students who are learning to know what operations to use for applied problems, the GOM is best. The final option for math progress monitoring is CBMmath Process. This assessment focuses exclusively on the individual steps that a student uses to solve a multi-step basic operation (e.g., 304+67+2598). This measure is best for students who have difficulty applying the right steps needed to solve such problems and are participating in intervention to build these skills.

Summary

FastBridge Learning offers a range of math progress measures designed to help students improve their overall math proficiency. Each measure is aligned to certain important skills. In order to select the right measure for a student, the teacher first needs to know what skill(s) the student needs to master next. Selected FastBridge Learning screening reports provide helpful information about each student’s current math skills. Once the skill area has been identified, the appropriate progress measure can be selected and used. Teachers are encouraged to review student’s progress data often (e.g., weekly) in order to learn whether the provided intervention is leading to desired skill improvements. FastBridge Learning provides progress reports that include graphs depicting student scores. FastBridge subscribers can get more information about how to interpret progress graphs by completing the online module titled Progress Monitoring in the Training section of the FastBridge website.

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.

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