Developing mathematical reasoning skills before and during secondary school is crucial to a student’s math mastery and overall academic success. Mathematical reasoning is the process of applying critical and logical thinking to a mathematical problem to come up with the right strategy to reach a solution.
Reasoning is often considered the glue that bonds a student’s mathematical abilities together. It is also sometimes viewed as bridging the gap between problem-solving and fluency, enabling students to utilise their fluency in accurately performing problem-solving. Because of its enormous importance in a student’s success in math, the development of mathematical reasoning is necessary, especially among secondary students.
Below, we explore the significance of mathematical reasoning for secondary math students and some simple but effective ways to enhance it.
Why is mathematical reasoning important for secondary students?
Generally, the term ‘reasoning’ refers to a thought process that produces a connection between known facts and a conclusion. In particular, mathematical reasoning is the process of tracing lines of inquiry to produce statements and form arguments that aid in reaching and justifying conclusions. It is a vital ability for all math students to have and must appear in every math lesson.
In essence, reasoning is necessary to establish a mathematical idea and provide proof of the truthfulness of such an idea. It is important for secondary math students, as it contains active, generative, and dynamic processes. It enables the students to structure their mathematical ideas actively and understand math ideas. Reasoning skills can also support the students’ complete comprehension of mathematics and help them develop creative thinking abilities.
Best tips for improving a student’s mathematical reasoning
When students have good mathematical reasoning, they can understand why certain mathematical functions work the way they do and how to use those functions to come up with the right answer instead of merely learning a memorised set of algebraic formulas. As such, every math student needs to develop their mathematical reasoning skills.
Although mathematical reasoning is not easy to learn, there are tried-and-tested ways to improve a student’s mathematical reasoning abilities more easily. Here are some of them:
1. Encourage them to ask ‘why?’
The most crucial way to teach students mathematical reasoning is to instruct them to justify their answers. If students can verbalise how they reached their answer, they can easily determine the logical thinking involved in arriving at their conclusion. As much as possible, the student should be encouraged to explain their thought processes when solving an equation.
2. Teach geometric proofs
One practical application of mathematical reasoning is geometric proofs. Basically, geometric proofs are a list of statements and reasons used to prove the truthfulness of a given mathematical idea or concept. To create geometric proofs, the students must first write down what they are provided within a geometry problem and what they suspect. In the second column, they must explain why every statement is true.
The best thing about geometric proofs is that they prompt students to look at mathematical problems in small increments instead of rapidly solving them in their heads without much thought. In that case, they assist the students in comprehending the reasoning behind solving the given problem.
3. Let them work with other students or with a tutor
To help students improve their mathematical reasoning, they should be encouraged to work in pairs or groups. Working together on a math problem allows them to justify to one another how they come up with an answer. They will also be able to examine and critique the reasoning of the other students.
Aside from working with their peers, students can also work with a reliable tutor to help develop their mathematical reasoning. As mentioned earlier, mathematical reasoning is a challenging skill to acquire. So, seeking some assistance or guidance from a professional math tutor could really help. Fortunately, math tuition is easily accessible for all students, both at the primary and secondary levels.
A successful math student should have good mathematical reasoning skills on top of basic numeracy skills. To succeed in secondary math, students must have the ability to come up with logical strategies that they can use to solve any given mathematical problem. While mathematical reasoning is not easy to learn, hopefully, the tips shared in this article can help your child develop their mathematical reasoning skills more easily.
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