Another “What Works!” post ~
After tutoring my eldest daughter through her high school maths course all the way to graduation, and now working with my junior high daughter in her maths course and doing middle school maths with my youngest, I know that maths matters … but it also can bring tears and the mutters!
Here’s 12 maths principles that I’ve seen work ~
- Maths needs daily exercise – much like having to walk the dog! My kids do 2 pages of maths exercises every day except for Fridays. We mix it with maths drills, times tables practice or word problems.
- Use manipulatives. Maths comprises of abstract concepts. Young children especially need to work with real objects. When teaching any new concept, start with real objects and teach with examples. Use blocks, Unifix cubes, real measuring jugs and scales, work with tape measures and rulers. Use number lines, pie pieces, apples and oranges. Whatever works, use it. Keep trying until you find the “one thing” that clicks with your child. Let your child practice with these objects. (Pop over to my free Maths pages for these manipulatives.)
- Take your time here at the physical level. Don’t rush. Make sure the child understands the concept well and is confident before going back to the books. If your child forgets, revise with manipulatives. If they get stuck, go back to manipulatives. This is vital. Confidence is a huge factor in maths success.
- Encourage mental maths muscles. Train your children to think maths problems. Exercises with number order (what comes before/ after a number), bonds (adding numbers to each other) and times tables are essential. This follows the manipulative stage. Train them to get the answer quickly. Speed and confidence here will make the rest of problem solving and other exercises a breeze! (Check through my mental maths pages here.)
- Do drills. Even just 2 minutes of drills (oral, physical fun or mental maths pages) daily will help ‘cement’ the maths skills. Do this before the maths book work.
- Make it physical and fun. Do fun physical workouts when ordinary drills and manipulatives are not working to combat tears and tantrums. Recite the tables while jumping on a mini trampoline, while skipping with rope, when bouncing a ball, clapping hands, doing hopscotch … it is fun and it stimulates the brain! Use playing cards and dominoes for fun maths drills and mental maths.
- Maintain the course ~ if it works. Stay on the same curriculum if it works. Don’t switch around too much. Each curriculum has been designed to follow concepts. Some conceptually spiral, each year developing the concepts to the next level. Jumping from curriculum to curriculum may cause your child to stumble across ‘new’ concepts without having the introductory work. Many moms have shelves filled with maths books and maths courses and they still haven’t found a good ‘fit’. May I suggest that you choose the best of the lot and supplement here and there with other exercises or examples. BUT, I also encourage you to abandon a book that does not fit (it may not have enough examples/ too many word problems and not enough clear explanations) with gentle grace and look for an alternative.
- Tutor high school maths. If you or dad can tutor, great. It worked for me and my daughter. If not, find a friend, student, retired teacher, high school student or professional tutor to help your child. This is especially important with high school maths. Don’t let maths tantrums and upsets cause you to ditch homeschooling! Often a 3rd party person makes a huge difference in a teenager’s attitude. The student must report regularly to the tutor and be accountable for the work they understand and the concepts that they struggle with. Often tutors are great for pre-exam revision. The tutor can prepare the student for the type of work to focus on and the questions to practice.
- Practise the skills. “Practice makes perfect” is absolutely true for maths. Many maths books lay out brief explanations, give an example, and then go on to the practice exercises. Generally most students need to practice with the introductory examples several times to completely understand the new concepts. When the child starts a maths problem, they have some doubts and questions. When they manage the examples and the initial, easy problems, they gain confidence. But they need to establish this process with a few more similar problems before moving on to more difficult sums. Where maths books progress too quickly to more difficult exercises, or provide too few similar practice problems, children lose confidence. If they haven’t “got it” with the easy work and then struggle with more complex problems, they become afraid. Fear forms into frustration which then manifests into anger. Supplement your child’s books with examples or go online to find similar work.
- Do maths early, when your child is most awake and fresh. Maths requires mental fitness and this is most often early in the day. My teens often put off their maths lessons because they didn’t enjoy it much, but when they finally had to do their lessons, they were tired and they struggled more. I advised them to do it first and get it over with for the day. For young children, maths and handwriting should be done at the table, early in the morning. We do our seat work (or disciplinary subjects = those 3R’s) first and then go on to read alouds and narrations.
- Estimations are essential skills! Along with mental maths and confidence, the most important maths life skill is to estimate within range. I only discovered this as an adult, but I find that it is perhaps the most underrated skill at schools. Teach your children to “guess” quickly and then “prove” their guess. It is fun, quick and it builds enormous confidence in their maths ability. This can be done as “living maths”; in the kitchen while cooking and baking, in the garden when laying out vegetable beds and planting seedlings in rows, while cutting material, making dresses or designing woodwork patterns, while packing away toys, doing hobbies and crafts, or travelling on road trips.
- Many children will always “hate” maths. Their brains are just not wired to excel in maths. However, maths literacy is vital and will greatly improve their independence and confidence in daily life. Stick to the most reasonable maths program and assist your child to at least master the basics. My artistic, creative daughters have been unhappy about maths for years, but I have not negotiated with them that they drop maths until at least grade 10. For matric, maths or maths literacy is a compulsory subject and your teen will still need the above skills. Our South African maths literacy course is excellent. It is real, relevant and within the ability of a ‘non-maths’ student.
I share this all with this background ~ My early childhood years of insecurity with maths made me literally throw up with fear, especially in high school! Then, when I was a student teacher, I was once assigned to a school’s maths teacher for all the grades 3, 4 and 5 maths classes. I spent hours and hours on my lesson preparation because I was terrified that I couldn’t teach maths. It quickly made me realize that the best method to preparation and understanding was lots of “scratching of pencil on paper” and using several different textbooks to see the different approaches to teach the concepts.
A brilliant mathematician does NOT necessarily make a great maths teacher! In fact, the teacher who may have struggled with maths may make a more compassionate teacher and will know exactly how they learnt the maths skills through practice.
When I tutored my high schoolers, I did the maths work for them (with them sitting watching and listening), then with them, and finally I sat next to them as they worked. If they were stuck, I would try another approach or break it down differently. Even though I taught these lessons, I didn’t always have time to prepare before hand, and so the two of us figured it out together. We battled, struggled, sympathized and encouraged each other as we went along. It was the one place in their independent studies that we were vitally connected!
Mom, you can teach your child maths! You do not need to be a maths whizz!