Tag Archives: mastery

Problems with Determining Math Grade Level for a Student

A common scenario involves a school official reporting out the grade level in math for a student. For example, a 7th grade student I was helping had tested at a 4th grade level. As a result, the student spent much of her 7th grade year working on 4th grade math.

There are a couple problems in establishing a grade level in math. First, unlike reading, math is not nearly as linear. The image below shows a breakdown of the Common Core of State Standards math categories, called domains. In a video, I use this graphic to unpack why it is more challenging to determine a single level of ability for math. In short, the reason is the student could be doing well in some categories and doing poorly in others. Second, the testing used to establish ability level can be problematic for the student. For example, the student may not have the stamina or attention span to endure a longer assessment.

If you are presented with a single grade level as an indicator of math ability, I recommend that you ask for a breakdown by category and how your student will be provided differentiation to address gaps. This is more appropriate than plowing through all of the math at a lower grade level.

 

Tagged , , ,

Asking for Examples of Mastery for IEP Objectives

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:

  1. 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)
  2. 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: solve the 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.

Tagged , , , , ,

Levels of Learning

Learning is not a singular threshold to be met. There are different levels of learning – a continuum (see photo below taken from the book Teaching Mathematics Meaningfully).

continuum of learning

A student demonstrating proficiency (fluency) is far different from a student simply showing some level of understanding (acquisition). I remember learning to drive a car with a stick shift. During acquisition (initial understanding) I was looking down at the pedals and the stick shift as I thought through the steps. It is not surprising that many students who only show acquisition of a math topic soon forget it. Despite this, the acquisition stage is often were math in schools resides.

203234-674x450-shiftinggears.jpg

This extends beyond math fact fluency to all math topics and the students should take the next step and demonstrate maintenance. To do this, I recommend that a curricular based assessment be given a couple of weeks after a student initially showed what is considered mastery – the student successfully performing problems aligned with a given math objective.

Below is a excerpt from the book with an explanation of the topics. I use this text in the math for special ed courses I teach at different universities.

0203191106.jpg

Tagged , , , , , , ,
%d bloggers like this: