Unpacking Math Standards Part 1

 

One of the things I've heard the past few years of my teaching career is to unpack math standards so you know what to teach.  It was a big deal at one school but over the years, especially since COVID, I see it as much more important. 

Unpacking the standards refers to looking at standards in detail so the teacher knows what the student needs to know, what they should understand, and the prerequisites needed to get there. In addition, one should look at various ways to represent the knowledge visually and common misconceptions students are likely to have. 

One thing I see time and time again is when students incorrectly subtract.  They have a problem like 81 - 37.  Instead of borrowing from the 8, they switch the 1 and 7 so they actually subtract 31 from 87 and end up with the wrong number.  I don't know where that comes from but it is one that I see frequently in middle school and high school math.

Now to break things down a bit further.  When deciding what students need to know, it should include vocabulary, facts and rules when doing the math so they are able to complete the concept, topic, or unit successfully.  As far as understanding, one needs to look at the big ideas of the unit, the concepts within it and connections so students learn the relationships among everything.

Teachers also need to determine what students need to be able to do and and how will they do it.  Furthermore, it is important to think about all the prerequisite skills needed to learn the current material.  Know what prerequisites are needed means the teacher knows if certain skills need to be pre-taught or retaught. I have a student, I had to go back to the basics with fractions because he had no idea how 2/6 was the same as 1/3 and couldn't find a common denominator for say 1/2 and 1/3.  He could use a calculator for fractions but since he lacked a knowledge of fractions, he didn't know if the answer was reasonable.

Teachers can find the visual representations or the manipulatives needed to help students learn the concept or material for the lesson.  In addition, when a teacher knows what the common misconceptions are associated with the concept or topic, they can clarify and help students avoid them.  Next time, we'll look at how to actually do all this.  Let me know what you think, I'd love to hear.  Have a great day.