Recently I had the pleasure of being asked to present at the 34th ANNUAL CONFERENCE sponsored by ORBIDA (Oregon Branch of the Dyslexia Association of America). My audience was made up primarily of special educators from local area schools. I was asked a great question. I thought I would share it here with the readers of my Blog and also tell you what my response was. The questions was whether I had identified any key concepts children needed to have in place in order to be successful in math. If I thought that there were these concepts, the question then became whether I used any of them as assessments to identify students who might need targeted interventions.
My answer was affirmative that I believe there were key concepts and that that they could be used to identify students who were likely candidates for intervention. I then went on to describe examples for my second grade students. This is the list I shared with that group:
1) The first concept is number sequence and seriation. I assess this concept by asking my students to count for me as high as they can go. Any of my students who cannot count to 100 raise a level of concern. If they can count to at least 100, I then ask the student to tell me what comes before or after targeted 2 digit numbers. Difficulty with this task also raises concern. Either students are having language difficulties or haven’t picked up the patterns present in our number system. Handing students a set of counters and asking them to count them backwards helps me check to see if it is a language issue or difficulty with the patterns of counting. This one also gives me some information about the child’s innate problem solving abilities. Sometimes the child will stare and me and not know how to proceed, other students will start with any number that comes to mind and count backwards from there.
2) Next, I check to see if students are able to subitize. For those of you for whom subitize might be a new word, the following definition comes from Wikipedia. “Subitizing, coined in 1949 by E.L. Kaufman et al. refers to the rapid, accurate, and confident judgments of number performed for small numbers of items. The term is derived from the Latin adjective subitus (meaning sudden) and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range.”
To assess this concept, I show students random pictures of sets of objects representing the numbers from 1 to 20. My object is to see if they are able to instantly recognize and identify the totals for these sets. The items represented in the sets have been arranged in ways that make it easy for students to group subsets and quickly calculate the total. For example, they may be grouped in chunks of fives or tens plus some extras. Any students having trouble instantly recognizing the total amounts in these sets would raise a red flag.
3) Next on the list is a check to see whether students have the ability to conserve numbers. For this check, I hand students a handful of around 12 two-colored markers. Students shake them up and drop them. I ask them to tell me how many of each color there are and how many markers there are in total. I then repeat this exercise. What I’m looking for here are those students who have to count the total each time even though nothing has been added or taken away from the original set of counters.
4) My next check centers on place value understandings. First, I find out whether students have 1 to 1 correspondence. I hand them a set of about 35 objects and ask them to count them for me. I observe whether they have some kind of organizing strategy like touching or grouping items to help them keep track of what has already been counted. If they count the set accurately, I ask students to write the numeral that represents the total items in the set. So if a student accurately records a total such as 35, I would point to the 3 in the tens digit and ask the student where he or she could find that 3 in the set of objects that has just been counted. For this assessment I am looking for those students who pull out 3 items from the set or say “thirty” but don’t express an understanding that the 3 represents 3 sets of ten.
There are more interview questions I use related to geometry, measurement, time, and money but I won’t list those here to keep the length of this blog to a manageable level. What are your thoughts? Have you found any others you would include? Would this change depending on the grade level?