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What is mathematics?
What is mathematics?
Mathematics, often referred to as math, is a broad field of study that involves numbers, amounts, shapes, and patterns. It helps us understand and solve problems using numbers and logic.
Why is math important?
Why is math important?
Math is important for many reasons, including:
Problem-solving: Math helps us solve problems using logic and numbers.
Learning: Math is important for learning things like science and technology.
Everyday life: Math is helpful for a variety of life skills including using money and cooking.
Jobs: Many jobs need math skills. It's very important in retail, science, tech, and business jobs.
Technology and science: Math is used to create new technology. It helps scientists understand big problems like climate change.
How do children learn math skills?
How do children learn math skills?
The ability to learn math is a skill that is hardwired early on in humans, as babies can naturally tell which group has more objects. As children grow and develop, math is learned through a mix of playing, hands-on activities, structured lessons, regular practice, visual aids, and social interactions. Real-life interactions and support from parents/caregivers and teachers play a big role in helping children understand and use math skills effectively.
Children typically develop math knowledge in a gradual order, starting with basic number concepts and counting skills. These skills include: stable order, one-to-one correspondence, cardinality, conservation, order irrelevance, abstraction, subitizing, hierarchical inclusion, movement is magnitude, and unitizing (see A Progression of Counting and Quantity for information on each of these areas). They then move through operations like addition and subtraction and advance to more complex topics like algebra. A list of math skills at different ages can be seen by clicking here.
What are some psychological processes involved in math?
What are some psychological processes involved in math?
Attention:
Focusing on math tasks and ignoring distractions.
Being focused on a mathematical task over time, which is important for working through complex problems or exercises.
Memory:
Remembering steps and math facts, like formulas or numbers, for solving problems.
Cognitive flexibility:
Switching between different methods to solve math problems.
Applying different strategies to solve various types of math problems.
Reasoning:
Using logic to solve problems and understand math ideas (e.g., using logic to solve an equation).
Understanding and using abstract information that represent mathematical ideas.
Confidence:
Managing anxiety and building confidence in math skills.
How can we develop math skills?
How can we develop math skills?
Developing math skills involves a combination of practice, strategic learning techniques, and learning effective study habits. Here are some strategies to help children develop these skills:
Build a strong foundation:
Make sure they have a good understanding of basic math like addition, subtraction, multiplication, and division.
Review old material to keep skills sharp and fill in any gaps.
Understand the concepts:
Make sure children understand the ideas behind math problems, and are not just memorizing steps and math facts.
Use visual aids like diagrams and graphs to help them better understand and solve problems.
Develop problem-solving strategies:
Schema-based strategy instruction teaches students to use diagrams to show relationships between numbers and to solve problems. The key steps are:
Problem identification: Students learn to identify what kind of problem it is.
Problem representation: Students turn the problem into a clear diagram that shows what's happening.
Problem solution: Students choose and use the right math operations based on the diagram and the type of problem.
Have children review and check work for errors. Checking solutions helps catch mistakes and builds on learning.
Start from the solution and work backward to find the solution path. This method can be useful for solving problems and improving flexibility of thought.
Learn counting strategies:
Use methods like group counting (grouping items into sets rather than counting each number) or skip counting (counting numbers in a pattern, like counting by 2s or 5s) to make counting faster and easier.
Practice mental math:
Regularly do calculations without a calculator to improve speed and accuracy.
Learn shortcuts to solve problems quickly.
Practice math problem solving:
Set aside time to practice math problems.
Regular practice helps learn concepts and improves problem-solving skills.
Use resources:
Use online apps, games, and educational websites that offer practice problems, tutorials, and interactive lessons.
Refer to textbooks and workbooks that provide explanations, examples, and practice exercises.
Apply math to real-life:
Use math in everyday activities, such as budgeting, cooking, or measuring, to see its relevance and improve practical understanding.
Teach others:
Teaching math concepts to others can help with your own understanding and reveal any gaps in your knowledge.
Practice explaining concepts clearly and accurately.
How can we support those with math difficulties?
How can we support those with math difficulties?
Pre-teach important language:
Make sure children understand the language used in math problems and give them time to understand the vocabulary used.
Use multi-sensory learning techniques:
Use a variety of ways to represent information, including visual aids (e.g., diagrams) and concrete objects/manipulatives, along with oral or written explanations.
Break down problems: Break complex problems into smaller, manageable steps. Solving each step individually can make the problem less overwhelming and easier to tackle.
Develop automaticity:
Provide opportunities for repeated practice to make knowledge more automatic.
In the resources section, see the handout on Supporting Fluency of Math Facts for information on activities to try.
Use aids:
Allow the use of calculators when the focus is not on computation.
Teach memory aids/mnemonics (e.g., BEDMAS, word walls, colour codes).
Post problem solving processes/checklists on a student's desk or in the room.
Have students highlight math operation signs and use graph paper to support visual-spatial organization and visual motor issues.
Overcome anxiety:
Use relaxation techniques and positive reinforcement to reduce math anxiety. Developing a positive attitude towards math can improve performance and confidence.
Some research shows that having a growth mindset for math is helpful for achievement.
Encourage seeking help when needed:
Teach students that they should ask educators, tutors, or peers for help if they don’t understand a concept.
Encourage them to join or form study groups to discuss and solve math problems together. Learning with others can provide support and different solutions as well as enhance learning and attitudes.
Resources
Resources
Math.pdfMath Instruction Handout
Math Problem Solving.pdfMath Problem Solving Handout
More information and resources can be found at:
Understanding why kids struggle with math
Mathematics: How to help your pre-school and school-aged child
References:
References:
Boaler, J., Dieckmann, J. A., Pérez-Núñez, G., Sun, K. L., & Williams, C. (2018). Changing students' minds and achievement in mathematics: The impact of a free online student course. Frontiers in Education, 3.
Boaler, J., Williams, C., & Confer, A. (2015, January 28). Fluency without fear: Research evidence on the best ways to learn math facts. youcubed. https://www.youcubed.org/resources/fluency-without-fear-research-evidence-best-ways-learn-math-facts/
Dweck, C. S. (2008). Mindsets and math/science achievement. Prepared for the Carnegie Corporation of New York-Institute for Advanced Study Commission on Mathematics and Science Education. Stanford University.
Jitendra, A. K., Star, J. R., Dupuis, D. N., & Rodriguez, M. C. (2013). Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment. Journal of Research on Educational Effectiveness, 6(2), 114–136.
Kuzle, A. (2019). Design and evaluation of practice-oriented materials fostering students’ development of problem-solving competence: The case of working backward strategy. LUMAT: International Journal on Math, Science and Technology Education, 7(3), 28–54.
Siller, H.-S., & Ahmad, S. (2024). Analyzing the impact of collaborative learning approach on grade six students’ mathematics achievement and attitude towards mathematics. Eurasia Journal of Mathematics, Science and Technology Education, 20(2).
Starr, A., Libertus, M. E., & Brannon, E. M. (2013, October 21). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences.
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