Many teachers struggle with assessing their students' knowledge of the basic facts, also known as fact fluency. The teaching of the facts through strategies is (hopefully) standard practice now, so students have learned why the answers are correct, and not just memorizing facts. It's so much easier to remember eight-ten strategies as opposed to 100+ random facts. However, all too often we assess fact knowledge with the dreaded "mad minute," or some sort of timed drill.
So, what's wrong with the notion of timed tests? Jo Boaler, a professor of mathematics education at Stanford University, wrote an excellent article for the NCTM's Teaching Children Mathematics journal (April 2014). I agree with her in that I believe that these tests are used with the very best of intentions, but research has shown that timed tests are one of the main causes of early onset math anxiety for students across the achievement range. This means that even students who may know their facts are stressed by the thought of these drill assessments. The reasons that I believe timed tests are still in use today are:
1. They are efficient in that the entire class can be assessed in a minute or less.
2. It's the way we were taught when we went to school, and hey, we learned the facts.
3. We don't know of any other way to do it.
Here are my arguments against these reasons:
1. The tests are not efficient (and not fair for sure!) if they do not give accurate results. Many students who know their facts may be so stressed over the thought of a timed test that they freeze up. We teach students the facts by using strategies, and then don't allow them time to use the strategies when we assess! Brutal.
2. There are many things that have changed since the time that we went to school. We have learned so much more about how the brain works, and teaching strategies have evolved, as our society has.
3. I know how to do it!!!!
The best and most authentic assessment to test fact fluency is 1:1. And it does not have to be time consuming at all. While your students are working on practicing their facts (worksheets, centres, games, etc) simply crouch beside one at a time and ask them 5 questions. (For example, in Grade 3: What's 4+4? 6+7? 9+1? 5+9? 8+5?) Keep track on a checklist, sticky note, or whatever system you use. This tells you whether or not the student knows the doubles facts, doubles plus one, one more than, making ten and using a known fact (if I know that 5+9=14, then I should be able to figure out that 8+5=13, which is one less than the previous fact). Do the same thing the next day with different facts. This can be done with subtraction, multiplication and division.
Another assessment that takes a little longer but is extremely valid is this: have about 12-15 flashcards of facts representing the strategies you have taught. Ask the student (one at a time) to spread out the flashcards and sort them according to the strategy they could use to solve the fact. Then ask them to name the strategies and then give the answer. Judge automaticity if they can come up with the answer in 3 seconds or less (don't set a timer :)) This assessment takes a little longer, but is a very clear measurement of which facts a students knows, as well as which strategies.
In Manitoba, we are required to assess mental math and estimation three times for the provincial report card. We have to remember that the "basic facts" are just one part of this section of the report card. Computing mentally (what is 45 + 88?) and estimation skills are to be included as well. More on this in the next blog.
OK, so I'm still thinking about Math Anxiety and how to prevent or overcome it. One way to prevent anxiety in math is to make sure that our students have a solid grasp of our numerical system. Our number system is based on tens (and so is our measurement system!), so it stands to reason that our youngest students must have a strong understanding of what ten is, and how using tens can help us with computations and estimating. Therefore, working with ten frames is EXTREMELY important for our Kindergarten and Gr. 1-2 students. How much is ten, and how can we partition ten? What numbers go together to make ten? Knowing these facts fluently will lead to ease with mental computations, namely the "Making Ten" strategy of addition and subtraction.
But let's not just do drill and kill. There are so many fun ways to learn and practice our 10 facts. Using ten frame manipulatives is imperative, and a topic that I've written about before (click here). I've also written about some of my favourite math apps (click here), but today's post will deal with iPad apps that strengthen students' grasp of making and partitioning 10.
The first app (shown above and at left) is called Make Ten+ and is available free from the iTunes store. It's actually lots of fun. Students must click a number at the bottom that goes with the top number to make 10. The game is similar to Tetris in that if the numbers in a whole row are not clicked after a certain time, they rise and you must clear them before they hit the top. Lots of fun, especially for Gr. 1-2 students.
The next app is extremely popular with all of the students with whom I've share it. Subitize Tree has several options, but the ten frame option is my favourite for K-Gr. 2 students. The sensei asks players to quickly subitize (say how many without counting) the number of objects shown when the doors on the tree open. If students correctly identify the number, they get a point. Four points sets free an animal that is held captive in the tree. The game gets tense, but not anxiety-type tense! It's available for $0.99.
Friends of Ten has six different games that can be played, and all of them involve ten frames. Students can count how many, fill in ten frames, make friendly numbers, and add and subtract. It would be a great math centre! $0.99.
The next app I'd like to tell you about is called What's Hiding and is shown above left. Students are shown a ten frame with counters on it. They must identify how many there are by counting as they touch the counters, reinforcing the matching concept that is so important for Kindergarten students. Then the ten frame is covered up and some counters are removed. Students must say how many are left, which we can use to teach the Making Ten strategy, and also the Think Addition for Subtraction strategy! These strategies are so important for Gr. 1-2 students! What's Hiding costs $0.99.
The last app is called Franklin's Friends of Ten. I'm not sure what Benjamin Franklin has to do with Making Ten, but his image is kind of cute! :) This free app involves students identifying the matching number to make 10. When the correct number is provided, fireworks go off. This is a new app for me, and I haven't tried it with any students yet, so let me know if you've used it with your kiddos. Feedback would be appreciated!
Math Anxiety was a topic at the NCTM Conference in New Orleans that I was so lucky to have attended this month. One of the sessions (of the 750 that I could choose from!!) was called "Convert Math Anxiety into Math Achievement," and was presented by Carol McGehe, a math content specialist. She presented some truths and myths regarding math anxiety.
I see educators differentiating their instruction so well in subjects such as ELA, Social Studies, Science and more, and yet, many teachers continue to teach in exactly the same way that they were taught themselves. One lesson to the whole class, followed by a worksheet or exercise from the textbook, and when all your work and corrections are complete, then you go to the math centre. The math centre is where technology is often used as a reward.
We absolutely have to learn to differentiate our instruction in math class! Technology should play a huge role in making math more relevant and creative, and not just as a reward when all the work is done. We have to stop creating anxiety by using timed drills and competition between students. We have to show our students that math can be interesting, relevant and even beautiful (look at music, art and nature that uses mathematics!). We have to stop using math as a punishment (stay in at recess and do this math worksheet as your negative consequence). We have to show our students the reasons behind the procedures rather than relying on memorization. We have to teach our students strategies for learning facts, and we have to continue to encourage our students to know the facts with automaticity - something many parents and media think we are not doing. We have to encourage discourse in our classrooms, beginning in Kindergarten. We have to be upbeat and positive about math in body language as well as words. And we need to dispel the notion that math is hard, boring and irrelevant to our world.
My next few blog posts will focus on ways to accomplish just that.
Travelling Curriculum Support Teacher