Maths Problem-Solving

More often than not, students who are good at quick sums and arithmetics may struggle to fully comprehend the nature of mathematical problem-solving. When maths problems are articulated with written words and comprehension, some of the foundational concepts students learn about maths get lost in the process.

Solving maths word problems often require us to consciously choose and employ strategies that encourage stronger critical thinking towards the problem at hand. However many students lack the metacognitive abilities required to solve the richer maths problems

Luckily, years of research and testing have led to ordinary students being empowered to solve extraordinary problems. Here is one of the many approaches we utilise to educate our students to solve complex maths problems.

1. Define the problem: Before students solve a problem, they need to know what it’s asking for. Oftentimes, students struggle with word problems as there aren’t specific mathematical operators that outline this clearly for them.

The purpose of this step is to clearly pronounce and identify the common denominators and key operators in the problem. Encourage students to list out the points of what they already know and highlight the parts that they’re unclear on. This will aid them to utilise the right strategies to fill in the gaps. Practically, here is an approach to help students better define and understand the problem.

Identify the important information from the noise:

Example question: Darius is collecting money for a local animal shelter. He starts with $2.50 of his own money, then his friend Boyd gives him $5.00 to contribute for the same cause. How much money has Darius collected for his local animal shelter?

While we can instantly look at the problem without really needing to know the names and the charity scenario as it is a very simple addition problem, students can struggle to determine what’s relevant in the information given to them.

By teaching students to sort and sift relevant information in a problem, they will know to simply add the two given numbers. A good way to practise this is to have students change the names and scenarios to show them that there will be no impact on the result. Then, they’ll realise that the names and scenarios don’t need to be a focal point while solving a problem.

2. Plan the approach: Once you have defined the nature of the problem, identify the strategies that you can use to go about solving this problem. Some strategies that could be employed are:

  • Guess and check: Students make an educated guess and then apply the answer back into the original problem. If their guess didn’t solve the problem, they now have an answer of what it can’t possibly be.

  • Visualise the problem: Visualising an abstract problem often makes it easier to solve a problem. Students can simply draw the problem in a way that helps them better understand the core of the problem.

  • Work backwards: Working backwards is useful if students are tasked with finding an unknown number in a problem or mathematical sentence. For example, Johnny went to an orchard and picked 6 apples. By the end of the day, Johnny came home from the orchard with 10 apples as he was gifted them by his friends. How many apples did Johnny’s friends give him? At the core of the problem, it is simply 6 + x = 10. By working backwards, students can easily solve this by:

  1. Starting with the number 10

  2. Then removing 6 from 10

  3. Leaving them with 4

  4. Then students can check to see if 4 will fit to replace x

3. Do the problem: Now that students have learnt to identify the problem and plan their approach, they work towards solving the problem But by launching into the problem without a targeted approach to keep each step in check, students will risk making silly errors. Here are some ways that we help students execute what they’ve learned:

  • Document the steps: Model the process of writing down every step taken to complete a problem. This will allow students to keep track of their thoughts, pick up errors and revise their steps before they reach a final solution.

  • Check, check and check again: Encouraging students to check their work as they go and once they have finished is a crucial strategy, not only in mathematics but across all learning areas. Embed questions such as:

  • Does that last step look right?

  • Does this step follow on from the prior step?

  • Are all the smaller sums in previous steps captured correctly?

  • Are the steps that I'm taking applicable to prior problems I've solved?

By posing questions like this, students will develop natural diligence toward solving maths problems.

Solving maths problems enhance a student’s ability to process information and to think creatively and critically. Although challenging, by applying various strategies and persevering, students will unlock their capabilities and experience the joys of solving real-life scenarios and objects in their learning. Above all, students with advanced maths problem-solving skills have a greater depth of being able to tackle all styles of problem critically and analytically.

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