When people don’t know…

It bothers me when people rally against something without getting all the facts first. I get it from the general public when I tell them my profession. I get it from stuck-in-the-past veteran teachers opposed to change. I’ve even gotten it from my own family. 

I don’t normally write about my work on this blog, but I had to this time. A voice of reason must be heard. 

Please view this video then continue reading. 

The People’s Voice video
What the woman is demonstrating is a strategy, one of many that students are exposed to, for solving a subtraction problem. It is a strategy, not a common core standard. The standards tell us what knowledge the students are to gain at a specific grade level, not how the student is to learn it. They do not specify a specific strategy to use either, except in the case of the standard algorithm. There are specific grade levels where the algorithm for each operation is appropriate and where it’s not. In most standards where strategies are mentioned it will say “…using various strategies such as a tape diagram, a number line, etc.” This gives students options. 

Furthermore, this strategy is taken out of context. It is a scaffolded higher level strategy. Students began concretely with place value blocks or place value disks on a place value chart, then moved conceptually to a number line. The strategy in this video is the abstract level that was built on the solid foundation of the other two, and is just one more scaffold up toward standard algorithm. 

Place value blocks show a solid grouping of ten ones in the tens rod and a solid grouping of ten groups of ten in the hundreds flats.

  

A drawing representation of the place valure blocks.

  

Each disk represents one unit within each place value block on the chart.

  
  

Number line ‘jumps’ are in increments of 1s, 5s, 10s, 100s, etc. to utilize mental math, a strategy not requiring paper and pencil to solve (10+50=60 a known equation based on place value knowledge).

  

The stand algorithm.

 
This standard (MAFS.2.NBT.2.5 for Florida Standards users, MA.2.NBT.B.5 for Common Core users. The wording is the same, only the label was changed.) requires students to “fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.” It, like so many math standards, does not specify which strategy the student absolutely must use.
I agree that ‘if it ain’t broke, don’t fix it.’ But what happens when it is an insurmountable wall. If traffic is backed up for miles and miles due to lane closures on your usual route, are you going to just stay stuck in it or are you going to look for other roads that will still lead you to your final destination? If you only know the one route, you’re pretty much stuck. But knowledge of the roads in the area gives you alternate route options. 

There really are some GOOD strategies being taught in mathematics these days. And the reason they seem strange to some of us is because we were taught ‘rules’. “Do the math this way because I said so.” But rules expire. 
Rule: use the “butterfly method” (cross multiplying) to compare two fractions. 

Expiration: there are more than two fractions to compare. 

In math instruction the right answer is still the objective, however we are now showing students more than one path toward that end, allowing them to use what works best for them and their learning modality. The strategies being taught are to help students develop a deep understanding of mathematics, giving them a broader road map as it were, rather than giving them a single path by having them memorize rules that can and will expire as they progress through math. Not every strategy is going to make sense or be useful to every student, but that doesn’t make it wrong, unless it yields the wrong answer. 

I was a terrible math student in school, all the way up through college math. I was locked in my thinking by the rules. But when I began teaching elementary math, I developed that deep understanding of the mathematical process and the integral relationship between operations right alongside my students. I’ve had far more ah-ha moments since I started teaching math than I ever did as a student. Math for me now is an incredible journey, not the foreboding obstacle it once was. 

That doesn’t mean I don’t use ‘short cuts’ like the standard algorithm. It means I use the most efficient strategy I am comfortable with to the given situation. Sometimes I don’t have paper and pencil to work it out ‘the old fashioned way’ so I need a fall back strategy. 

That is what today’s math instruction is all about. Giving students options. Helping them to be successful in finding the right answer by various means rather than locking them into only one method that might not always work for them or their situation. 

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1 Comment (+add yours?)

  1. So Much To Choose From
    Dec 12, 2016 @ 17:24:04

    Being a retired teacher, my pet peeve is people not knowing the difference between a fact and an opinion. I don’t like the manipulation people do to discount their children’s learning. I did propose a few wrong moves as a teacher. But usually, I took students on the most direct route to learning a concept.

    Reply

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