More on Math... Math Sense: Stage 3 Help
So far, I have covered math in the following posts:
I have found that, despite the claims of the Everyday Math curriculum, my daughter doesn't have a "math sense" because she isn't required to practice mental math with numbers often enough.
The resources that I describe in my Math Tutoring post require very little input from parents. The drills at funbrain will help them -- let's call this first stage help in terms of parent involvement -- but it is only one part, albeit the one part that is usually missing from school for reasons described in the post. The learning at aleks will help deepen and broaden their knowlege of math concepts and help cement those concepts -- let's call this second stage help in terms of the parental time needed in order to see an improvement.
If you don't have a lot of time to devote to math at home, the first two interventions will help if your child is struggling with math. They will also help your accelerated math student. Parental input consists of going up to the computer, reading an explanation of the concept if they have trouble with it, and walking them through it. However, neither solution necessarily makes the bridge to "math sense." Does the answer fit the problem?
To get to this point, more parental intervention and interaction is required, or stage 3 help. I would recommend taking 5 minutes at breakfast or 5 minutes at dinner on a daily basis. The stategy that I am advocating comes from Five Easy Steps to a Balanced Math Program, and it is from the chapter: Math Review, Computational Skills, and Mental Math describing mental math and the authors explain in the excerpt:
The purpose of Mental Math is to provide students with mental practice in computing basic number facts and combining mathematical operations. The teacher dictates a string of numbers and operations that students compute mentally to determine the final answer.
For example, the teacher calls out the number string, “2 x 4 + 8 – 6 ÷ 2,” pausing briefly after each operational step, so that it sounds something like this: “Two times four…plus eight…minus six…divided by two.” At each pause, students have a chance to calculate mentally before the teacher moves on to the next step, but they don’t write anything down until the final answer. In the example above, students calculate the answer in their heads and write “5” (hopefully) in their math journals right beneath the Math Review problems of the day.
The answer is not given yet, however. The teacher repeats the same problem to allow students who might need a second chance to succeed. Those who think they know the correct answer are asked to calculate again to make sure. The teacher then asks the students to announce the solution, and the answer is verified by computing the problem aloud in increments to help those remaining students who were still unable to do it. In this way, everyone stays involved.
And, if you really want the whole kit and kaboodle, then this next step is for you. Again, from the same book, providing a math review:
An effective Math Review component to a balanced program does not come about simply by writing a different set of random arithmetic problems on the board each day. Instead, the same types of problems students see on the board on Monday reappear throughout the week. Students understand that these problems provide opportunities for practice of problems they have already been introduced to, and that they may receive additional guidance and instruction as needed from either their teacher or their peers.
Students also understand that their progress will be assessed weekly by encountering the same kinds of problems on the Friday Math Review quiz. If we want students to maximize their learning of particular math computational skills, it is necessary to avoid introducing them to new kinds of problems within the same week and to instead provide them with consistent practice of the same types of problems until they are learned.
Math Review presents a deliberate progression of mathematical concepts and computational skills that increase in difficulty throughout the school year. Problems of the same type recur week after week until the majority of the class masters them. Only then does the teacher introduce a new concept or skill, which replaces the one the students have sufficiently learned. In this way, new types of problems are cycled through Math Review as the year proceeds.
If students need to review any concepts at some point later in the year, those types of problems can again be included in Math Review. However, if students practice a particular computational skill until they thoroughly understand it, it becomes less likely that they will need to be re-taught that skill in the future. They can later revisit skills and concepts and build on prior understanding.
They give an example 5th grade math review template:
So, as a parent, you should check out their homework and try to create at least two problems that build off that homework, if you can. But the key in doing this is "correct the problem together":
The key to processing Math Review effectively is to emphasize number sense and reasonableness of answer. In other words, the goal is to help students determine whether their answer is reasonable in the context of the particular problem and if it demonstrates an understanding of our number system.
When teachers have successfully created a classroom climate where mistakes are regarded as a normal part of the learning process, it is much easier to teach their students how to do an “error analysis” when Math Review answers are incorrect. We define “error analysis” as helping students (1) identify the part of the problem done correctly and (2) pinpoint the part of the problem where they made an error.
This, clearly, is the whole package that parents can't implement fully unless they home school. (And if you do homeschool, or if you are an interested parent, I highly recommend getting this book.) However, parents can implement a part of it. (Again, some districts may be doing this. My own particular district seems to be making strides in recognizing the importance of doing mini tests now, and I'm currently getting the test back with a sheet that shows where my daughter should be according to the curriculum and where she is -- transparency is key -- but I've got a lot of years to make up.)
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