My state is currently rewriting standards and the state test to change the way they look at things. Rather than focusing on standards, they are looking at achievement levels.
I know someone on the committee for math and he's shard a bit of information which makes me a bit concerned.
According to him, one change is looking at multiplication using the standard algorithm. He said the standard algorithm is for the two numbers lined up, one directly above the other but many teachers are choosing to teach the lattice method because students catch on to that faster.
The long term sub in the 5th grade commented how so many of her students struggled with the two digit by two digit multiplication. I offered to come in to teach the lattice method. After 20 minutes, her students had the basics. The more advanced ones were off doing two digit by three digit or even three digit by three digit but they all got it.
I suggested to a friend that since lattice is being taught more and more it could be considered a standard algorithm especially as most tests have students provide the answer but do not have to include the work. The test doesn't know which method is used, only if the answer if right or wrong.
I show several different ways to multiply binomials and lattice is one of the methods I use because many of my students already know it so its a short hop, skip, and jump to using it in algebra. They always get it set up properly but mess up because they do not watch for signs.
So if tests only want the answer, why even throw phrases like standard algorithms into the standards. Why not just use acceptable algorithm instead since in reality there are so many different ways to multiply numbers together. It seems that even state standards are still being caught up with processes rather than real understanding of the material.
I would argue our testing should move towards being able to explain the steps of the algorithms in addition to using the algorithms to test understanding rather than just the mechanics. Most tests have moved away from hard copy to computer based so we should be able to design tests which allows us to check their understanding of why certain steps are used.
There are times I feel like we are wagging the tail of the dog rather than letting the dog wag its own tail. I'd love to hear what your thoughts on this topic. Have a great day.