Teaching mathematics has come a long way forward from the older times. Modern mathematics has been a product of teachings since ancient times by the Chinese, Indians, Arabs and Greeks. However, we have drifted away from many of the older techniques and invented a set of rules to memorise things rather than express them.
Though in recent times, the teaching of basic maths underwent a tectonic shift by introducing approaches like number sense, it still carries many fixed norms. These practices can be termed as a set of unproductive practices above all.
- The reason for basic unproductivity
No matter how far maths teaching has reached, the basic mathematics lessons still depend on memorisation and recall. So it prioritises automaticity, speed, accuracy and the right answers.
Reaching the right answers is indeed a top priority. Recalling speed and automaticity will result in mathematical fluency in the long term. But students learn these techniques at the expense of ‘procedural fluency and mathematical reasoning. Such unique techniques proved remarkable in a student’s maths learning process. But, of course, you can also create such visualisation in Tableau. If you cannot operate Tableau yourself, take a Tableau assignment helpfrom professional sources.
- A short glimpse of the changes needed
A recent study on mathematical teachings done by reputed professors shows that popular teaching practices of mathematics teach us blind recalling and unquestionable adherence to formulas and sets.
The study suggests that we must design basic maths focusing on flexibility, curiosity and wonder. That’s the only way mathematics can become an adaptable and powerful tool for sensing the universe.
- Take verbal explanations bypassing visual strategies
- A misplaced assumption
It is a misplaced belief that once a maths strategy is explained verbally, students will make some sense of it. But their attitude urges students to ‘understand as per the teacher’s wishes. But you need experiences developed through time and tenacity to visualise those numbers. So a good lecture and explanation are not good enough.
- Adopt different visualisation techniques
According to the researchers, we must learn to use a more liberal technique of number visualisation. One major tool is to use the ‘quick look cards’. It shows students several dots or pictures of familiar items of everyday life. For instance, after pointing at an egg full of plates, you can ask questions like whether it has four eggs in two pots or two eggs in four pots. You can also use manipulatives to get a sound understanding of how different mathematical strategies work.
- Use sliding techniques to teach maths
There is a sliding technique called Splat. The technique was designed by a teacher named Steve Wyborney. He is a coach of K 12 in Oregon. The technique asks a student to identify the number of dots in multiple slides. Then, the student has to count the dots on each slide.
Then he asks students to follow a blob covered in the shape of an amoeba. Then students arrive at the right or wrong conclusion by counting on their strategy.
- Follow numerical order in teaching maths
- Isolating numbers from its applications
The common tendency is to teach numbers in ascending numerical order. We always take a numerical approach for each application of addition, subtraction, multiplication and division. We begin at 0, then 1, 2, 3 and so on. That’s how we learn time and numerical tables. But, with this technique, students learn these facts as ‘objects of isolation’. Right at the beginning, it teaches us superficial knowledge of mathematical operations. It is a stumbling block for a student’s understanding of maths and suppresses his achievement significantly.
- Teach them the right derivation technique
Research shows that commencing maths learning with the foundational sets like the 2s, 5s, or 10s will not only familiarise them with the numbers but also know about the facts derived from them. For instance, if you learn about the 5s, you can split a multiplication of 8×7 into 8×2 plus 8×5. It will help them tackle more formidable problems like 8×56.
- Dealing with squares
After these fundamental operations, students can move square sets like 8×8 or 7×7. Squares are harder and more challenging. It’s also relevant for algebra, measurement and higher geometry.
- Applying a single strategy for problem-solving
- Learning subtraction first
One of the widely accepted practices in basic maths is learning subtraction first. For example, suppose a problem states 20-11=? Here, the common count is to start from 11 and reach upto 20 by adding single digits. The approach is undoubtedly good and proved its worth in the past. But it is one technique amongst many. You ask students to inhibit their larger reasoning skills if you ignore the others.
- Applying the compensation strategy
You can teach them to start with other strategies, such as compensation. For example, take a set of numbers and subtract them, like 20-11. Then convert it to 20-12 and add 1 with the final answer. It will help students to break the subtrahend and the minuend. For instance, you can split 20 into 11 and 9. Then do 11-1=10, and subtract it with 1 to reach 9.
- Mastering and recalling facts excessively
- The common practice of maths problems
We are habituated to seeing pages after pages packed densely with numbers, tables and formulas. It seems that mechanical dexterity and speed are a priority over sustained procedural fluency. The experts observed that practising more than 30 problems on each maths page is a worse nightmare for students. It leads to the common perception of ‘we hate maths’.
- Reasoning tests are better than memorisation
Normally, we put excessive emphasis on memorisation. This is because it leads us to learn calculation tricks. For instance, beginners would use their fingers to make quick multiplication with 9. But the same technique does not apply to other numbers.
But teaching a solid reasoning strategy would help them develop a common theme for all calculations. For instance, 58+69 is a big calculator for a kid. But teaching them to ‘count in tens’ is much easier. Like they first add 1 to 69 and then subtract 1 from 58. It transforms the problem into 57-70. This is how a calculator becomes much more reasonable with number manipulation.
- Focusing too much on speed
- Faulty experiments with speed contests
Speed tests and contests are one of the most popular trends in the mathematical world. But experts suggest that it drives a student’s fluency in the opposite direction. As they grow up, they tend to avoid complex mathematical problems and always find quick fixes. Automatically they restrain themselves from practising time-taking strategies. But solving complex problems step by step develops his reasoning abilities much more.
- Balance speed with reflection
A possible way out is to balance reflection and speed. You can use it with a mix of fun elements. You can also adopt games to reduce stress and focus on skill development in multiple ways. Here is a popular example.
Let’s play a game called ‘Tens Go Fish. Here each player has to choose two cards together. But the added digits would be 10. They don’t need to match pairs. So, if one student has 7, he can ask his opponent for a 3.
- The pressure of timed tests
- Tests that prioritise a single answer
A major roadblock to a student’s mathematical fluency tests always seeks a single answer. For example, they ask a second-grade student to perform 50 multiplication problems in 5 minutes. It creates a quick assessment fluency. But they are much poorer ways of measuring flexible reasoning in mathematics. Naturally, it stymies clear and critical logic; reinforcing ideas such as maths is unforgiving and dreadful.
- Apply assessment strategies
A viable alternative to learning mathematics is using different assessment strategies. Here are some options we can apply to students.
- Interviews of peers
- Journaling of problems
- Asking open-ended questions
- Taking a storytelling approach to learning maths.
These are simpler yet innovative approaches that can save a student from encountering the harmful effects of time-based tests and memorisation. Also, they offer a change in perspective. Now the attitude shifts from “solve your problem” to “how did you solve your problem?”.
Try to isolate them from the idea that only the ‘right answer matters’ to ‘individual communication and thinking matters.