So far I’ve focused on summer math for elementary students who are ahead and for those who are right on track. What about students who are behind and need remedial work to catch up? Summer is an ideal time to work on math concepts away from the pressure of school. Creating an environment where math is fun and relaxing is important for all students but especially for those that have low confidence in math.
If you have a student who is behind in math, its important to look at where the problem really lies. If they have a good grasp of basic concepts but just need a little more fluency with basic math facts, then games are an ideal way to practice without stress. You can use workbooks for more advanced topics like long division or fractions, but keep it short and simple: only a few problems per day. Dense pages of similar problems can lead to fatigue, and tired students make mistakes.
In many cases though, the problem isn’t just an issue of practice, but a true lack of understanding. Unfortunately, when a student doesn’t understand basic concepts there are no short cuts; they need one-on-one attention with a focus on really building number sense rather than memorizing mindless procedures. Hands-on activities should be the first resort for remedial students, and so enters my favorite math manipulative… the C-rod.
Cuisenaire rods (or C-rods for short) are one of the most amazing math tools of all time. Developed in the 1920s by a Belgian school teacher and popularized in the 1950s, the set of colored rods representing numbers 1-10 (each rod a different length and color) can be used to teach almost any basic arithmetic concept. I like to start little ones out with simple games like identifying rods by number, building a staircase of numbers by laying the rods in order, and hiding one of the rods to guess which one is missing. Basic arithmetic begins with the simple idea of adding one, then by identifying pairs that add up to 10, a foundational concept necessary for the kind of regrouping needed for addition and subtraction of larger numbers.
Why C-rods and not coins, counting bears, or other discrete objects? C-rods move children towards thinking in terms of whole numbers, rather than seeing each number as simply a collection of ones. It’s a subtle distinction, but an important one for developing the ability to break numbers apart and put them back together again. It seems counterintuitive, but counting is inherently inaccurate, and the faster you can move a child away from counting, the better. Cuisenaire rods are great for basic concepts, but also really shine when it comes to more advanced topics like multiplication, division, and fractions.
It’s hard to understand how they work without a real demonstration, and so rather than try to describe how to use them in words, I like point people to Education Unboxed, a website wholly devoted to teaching with cuisenaire rods. Rosie, the site’s creator, uses her own three daughters in these charming and engaging videos to demonstrate how to teach everything from addition to fractions to decimals to basic polynomial factoring. I recommend watching the videos in advance and teaching your child directly, but if you are really short on time, you and your child can watch the videos together to try and work through the concepts.
What about Khan Academy videos? This is a topic for another post, but in general Khan Academy is incredibly overrated. The videos on their website mostly show procedures and tricks, and do not teach for understanding. While this can be somewhat useful when reviewing material that was once mastered a long time ago, it doesn’t really help a student who never understood the concepts in the first place.
If you want to get started with cuisenaire rods I recommend a basic set of 155 rods for about $20 on Amazon. The Education Unboxed videos are available for free.
Next up: Summer Math for the advanced high school student!