Diagnostic Assessment
I have access to two diagnostic assessment tools. I use i-Ready assessments for all of my students and ALEKS assessments for my most advanced eighth graders, who take an algebra enrichment course with me in addition to their regular math class. i-Ready score reports provide a great deal of information about students’ levels of conceptual mastery in relation to grade-level standards and expectations. In addition to offering class averages across four major mathematical domains—number and operations, algebra and algebraic thinking, measurement and data, and geometry—reports can also show individual student scores on the test. These scores are extremely useful for instructional grouping and differentiation, especially at the beginning of units. For example, when the seventh graders begin working on an algebra-based unit, I will know that the third scholar listed (who earned a 511 overall) should probably be in the second-highest instructional group despite his or her top-quintile overall score on the beginning-of-year (BOY) diagnostic.
Average class score by domain for the seventh grade. This graph is helpful as I plan my units for the year because it provides insight into which broad domains of mathematics the class as a whole is likely to find most challenging and most intuitive. Such information can help to inform, among other things, how much time I budget for introductory activities at the beginning of a unit.
Individual student performance data for the seventh grade. These data are even more helpful than the class averages because they help me to understand which of my scholars will need the most support to master grade-level standards and which of my scholars will benefit most quickly from extension activities that move beyond grade-level content. Notes that the third scholar in the list, whose individual data are featured in more detail below, is weaker in algebra than in the other three domains.
Detailed i-Ready score report for the third seventh-grade scholar. The graph above and table to the right provide much greater detail about this scholar's present abilities and likely instructional needs. Thus, this score report is a ready-made tool for differentiated instruction. My knowledge of this scholar's diagnostic data will help me to channel exactly the right kind of support toward him or her throughout the year. Such support will focus on (but not be limited to) making connections between algebra (his or her area of weakness) and the other three domains (his or her areas of strength).
Each January, my students take an i-Ready middle-of-year (MOY) diagnostic assessment. I create "heat map" comparisons of the difference between all of my scholars' MOY and BOY scores in each domain so that I can easily identify students who have made particularly strong growth in an area and, more importantly, scholars who may be “sliding” and need additional differentiation and other supports to continue progressing. Significantly, i-Ready scores offer an indication of student progress against grade-level standards, which is very useful in terms of assessing my own instruction and preparing students for end-of-year standardized testing.
Heat maps of class i-Ready growth through January of 2017, created with Microsoft Excel. Scores in green represent above-average progress, while scores in red represent below-average progress. Looking at which columns are most green and red helps me to visualize which domains are good candidates for whole-group activities and which might be better addressed with differentiated small-group and one-on-one remediation.
The eighth graders in algebra with me also take a diagnostic test through the ALEKS platform. This assessment, called a "knowledge check," is used to determine student readiness to learn each new topic. Students take a new knowledge check after each period of five hours they spend working in the program. ALEKS offers excellent data visualizations to help teachers plan instructional activities. For example, shown below is the trademark "ALEKS pie" with color-coded slices representing different mathematical domains. Based on the program's analysis, 91% of my scholars would benefit from practicing how to write an inequality that describes a real-world situation. This sort of assessment data helps me to identify sensible groups for instruction and create high-leverage mini lessons that reach scholars precisely where they currently are.
ALEKS pie with instructional opportunities. The relative size of different wedges represents how much content students need to master within each domain to achieve complete mastery of the Algebra I learning standards. The amount of each wedge that is shaded represents how much of the domain students have currently mastered. ALEKS data is a critical component of my instructional planning for algebra lessons because it allows me to differentiate instruction so effectively.
Significantly, each eighth-grade algebra scholar can always view his or her personal ALEKS pie (which looks identical to the one above except for the amount of shaded area in each wedge). Students get very excited as they get close to filling in an entire wedge and often prioritize topics within that domain to achieve their goal more quickly. This ownership of their own progress generates a great deal of investment in their success within ALEKS; indeed, ALEKS was my inspiration for giving all of my scholars more control over their own learning path in i-Ready (see the page on Student Investment for more information). Furthermore, personal ALEKS pies help me to differentiate instruction for individual scholars in addition to small groups. During a typical algebra lesson, I have multiple short, one-on-one check-ins to help scholars master topics that are proving challenging for them. The fact that ALEKS diagnoses these learning gaps automatically leaves me with much more time to plan effective instruction that will fill in the gaps.