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.
Many teachers struggle daily with differentiating their math instruction in order to meet the needs of all the learners in their classrooms. Guided Math is one way to provide the differentiation needed, as it allows the teacher to work with small groups of students while the rest of the class is engaged in meaningful math tasks. There is no cookie cutter solution, however, and teachers must find the method that works best for them. Here are a few structures I have learned about, based on a 75-minute math class (in Manitoba, math instruction is recommended to be 15% of the school day for Grades 1-6 and 17% for Grades 7 and 8).
1. 15 minute mini lesson, followed by 4 work stations. One of the work stations is with the teacher, and the other 3 are practice stations (math games, using manipulatives, math project, math literature, math with technology, etc.). Students spend approximately 15 minutes at each station, and students are grouped by like ability. Students rotate through each station once per class.
Photo credited to: Enoch Lau
2. 30 minute lesson with the whole class, which may be teaching a problem solving strategy or mental math activity. Students then choose 2 math stations that they work on for the next 45 minutes (20-25 minutes per station). Students make the choice themselves, but must go to all the possible stations within a 1-week period. Teachers pulls 3-6 students at a time to work on a math outcome that needs review or extension.
Photo credited to: kfergos Photo credited to: MrSchuReads
3. Students have been taught to start a math task independently (such as Nifty Number, Toad Code, Math jobs) or there is another adult in the room (co-teacher or Educational Assistant). When the task is completed, students go to a math work station of their choice. While this is happening, the teacher is calling 3-6 students together to work with him/her on a math topic.
There are lots of options about what the work stations or centres look like too.
A=At Your Desk (independent work or reading math literature)
H=Hands-On (using manipulatives, working on projects, etc.)
L=Learning About Numbers
D=Doing Math (practice with a new strategy)
Math Daily 5
Math by Myself
Math With Someone
Writing About Math
This topic is so huge! There's no way I can write about it in one post. I'll be posting more info at another time. Watch for it!
This was the best week in the whole year, probably, as far as a travelling teacher's job goes. The fall colors were absolutely stunning, and I was in 7 different schools this past week, so I had many opportunities to marvel at this beautiful country we live in.
Today I'd like to discuss screencasting. A screencast is kind of like a screenshot, except that screencasts contain video and/or audio. Explain Everything is a screencasting app available for iPad and Android. I have heard teachers say that if you could have only one app in your classroom, then Explain Everything is definitely the one you would choose. At only $2.99, it's a real bargain, and you get lots of bang for your buck! There's a little video on their site that explains how it works. My colleague Amanda Smith (@Mandy_S_24) created an awesome tutorial that I also recommend checking out.
Here are some ideas for ways to use Explain Everything in your classroom.
1. Assessment: Ask your students to create an Explain Everything video to explain which personal strategy they would use to solve math questions or solve problems.
2. Projects: Students create a screencast to showcase their learning on a particular topic (animals or habitats biographies, science experiments, etc).
3. Flipped Classroom: Teachers create screencast for students to watch at home as part of a flipped classroom assignment, or for students who were absent from class and missed a lesson.
4. Portfolio: Students can create video on EE to save to the digital portfolio. Take a picture of the book they're reading in Guided Reading class and record themselves reading, using decoding and/or comprehension strategies, and timing fluency.
One of the best features of Explain Everything is that the project can be saved as a photo or video, uploaded to Dropbox, YouTube, or Evernote, and then you may use the links to embed the project into a class blog, wiki, etc. I'm sure there are many more applications that I haven't considered yet, and I'd love to hear feedback from others on how they've used screencasting in their classrooms.
Travelling Curriculum Support Teacher