The students loved playing the game, it was engaging so they practiced the counting out money, I was able to collect data, and I was able to differentiate. When I co-taught a Consumer Math course, I would assign a para (instructional assistant) to facilitate the game with a couple students and to collect data.
To ensure the IEP team is on the same page as to what mastery of an objective looks like, the person writing the objective can take two steps:
provide an example problem that would be used to assess mastery (and the example problem would have the same language as used in the objective)
provide an example of a response to the example problem cited above that would be considered mastery level work
The graph below is not data. A graph is a representation of summary statistics. This summarizes the data.
The chart below does not show the actual prompts, e.g. what number was shown to Kate, but it does show the individual trials. This is data, with a summary statistics at the end of each row. Here is a link to more discussion about data, with an example of a data sheet I use.
The data shown below addresses the student’s effort to solve an equation. Problem 21 is checked as correct and the error in problem 22 is identified. I can use this data to identify where the student is struggling and how to help. NOTE: the math objective would use the same verb as the problem: solvethe linear equation.
The excerpt of a data sheet, shown below shows trials in a student’s effort to compare numbers.
Data below shows a student’s effort to evaluate integer expressions.
This applies to all areas beyond math. The chart above or the data sheet I linked above show data sheets that indicate the prompt and the results, with notes. For example, if I am asking my son to put on his shoes, each row of the data sheet is a trial with the outcome and notes.
Here is an example of what data collection can look like. (The IEP objective should have been indicated on here as well.) It shows the data, any prompting from the teacher (P with a circle around it), notes and at the bottom is 3/9 for 33% correct.
Also note that I was working on finding the value of a set of nickels and pennies only before moving onto other combinations of coins and more coins.
List all the steps for the objective. Use this table (above) as a pretest to identify gaps.
Provide instruction on the gaps. In the photo below I used color coding to show what to multiply and scaffolding to align the digits in ONES and TENS place. NOTE: I provide the problems with some steps already completed to focus on the steps for which gaps were identified.
After providing instruction on the steps with gaps data is collected on mastery of these isolated steps. NOTE: The problems are identical in nature to the gaps and the problems used in instruction. (Link to the data sheets – WORD so you can revise.)
The graph shown involves derivatives – a calculus level topic. Before getting into this heavier mathy stuff, consider the title of this post and the other content presented on this blog. Making math accessible to all students is not a special ed or a low level math thing. It is a learning thing. This artifact is what I drew to explain the math concept to a student in calculus to help her grasp the concept as well as the steps. The following are strategies used.
color coding – each of the 4 sections written in different color
connecting to prior knowledge – the concept of velocity was presented in terms of a car’s speed and direction (forward or backing up)
chunking – the problem was broken into parts and presented as parts before exploring the whole
multiple representations – the function was represented with a graph, data (1, 2, 3, 4, 5) and a picture (at the bottom)
As for the mathy stuff, the concept of velocity was address by its two parts: speed (increasing or decreasing) and direction (positive or negative). The graph was broken into the following parts: decreasing positive, decreasing negative, increasing negative and increasing positive. Each part was presented with possible y-values (data) and the sign. The most intuitive part is increasing positive which is a car going forward and speeding up.
I find that when I provide intervention, this approach especially by addressing conceptual understanding is effective as the students respond well.
In special education there is a tool called a task analysis. It is a formal approach of identifying the steps taken to demonstrate mastery of a skill. For example, putting on shoes with Velcro straps involves the following steps: get shoes, sit on chair, match shoes with feet (right to right), insert foot into respective shoe etc.
I have applied this approach to general curriculum math topics from counting money to solving using the Quadratic Formula. Below are the iterations of my task analysis for the objective count TENs, a FIVE and ONES (dollar bills) to pay a given price. The first shows a rough draft of notes I took as I actually counted out the money, going through each little step. The second shows the steps written out on a task analysis table I created. The third shows the final, typed version.
The table is used for assessment, collection of data and progress monitoring. The steps that are problematic can be targeted individually, e.g. skip counting by 10s.