Posted in Teaching mathematics

5 Tips to Help Students Understand Math

Math is the language of the universe. If one were to excel in science and know the secrets of the universe, he needs to have a concrete understanding of math. As teachers, we all want our kids to succeed in math. However, it is our duty to give them the material, help them apply skills, and build their concepts. It’s imperative that we focus on making sure that our students understand the material rather than just memorizing it. In this article, I am going to highlight five tips that come in handy for students to understand math and grasp basic concepts.

Create a Perfect Class Opener
School is often boring for students. The reason for that is the approach of teachers when teaching their students. If the teacher sets a precedent that the aim of coming to class is to rote learning whatever is taught to the students, the ambiance will automatically become dull. The first five minutes of a class set the tone for the entire lecture, which is why teachers need to take a creative approach and opt for an effective class opener.

Solve the Problem in More than One Way
We have to understand that every student is not equal. Our brains are designed differently. If a certain student is able to grasp the concept taught in a certain way, it doesn’t mean that every student might have understood that concept. The best way to approach this problem is by showing the students different ways they can solve a problem and letting them decide the best way that works for them.

Raise the Bar for Them
Meaningful math education goes far beyond the contents of the book. Teachers need to motivate their students and make them understand that they need to set higher goals for themselves and create room for improvement. With the internet becoming a powerhouse for learning, teachers can make use of some helpful courses like MathXL for students that contain digital information in the form of videos, animations, examples, and more.

Show the Application
Making students learn a concept is one thing; showing how it is implemented in real life is another. In a perfect world, teachers would be able to demonstrate how every concept is implemented, but they should be taking this approach whenever they can. When students see how math is implemented in the real world, it will become much easier for them to grasp confusing concepts.

Finish the Class on a High Note
Just like the class opener is an important way to set the tone for the rest of the class, you need to finish your class on a high note so that students feel motivated that they have learned something. The last five minutes of the class are critical when it comes to making sure that students have understood everything, and they have a clear idea about the homework. You can do a quick assessment to find out how much the students have learned from the class and discuss future tasks so that there is no confusion.

Posted in Math blogs

Top 20 Math Posts and Pages in 2012

The thinker

I blog in order to organise what I think. And I don’t think I’m succeeding judging from the range of topics that I have so far written since I started Math for Teaching blog in 2010. Here’s the twenty most popular math posts and pages in this blog for the year 2012. It’s a mix of curricular issues, lessons, and teaching tips.

  1. What is mathematical investigation? – Mathematical investigation refers to the sustained exploration of a mathematical situation. It distinguishes itself from problem solving because it is open-ended….
  2. Exercises, Problems, and Math Investigations – The quality of mathematics students learn depends on the mathematical tasks or activities we let our students engage in….
  3. What is mathematical literacy? – Mathematical literacy involves more than executing mathematical procedures and possessions of basic knowledge that would allow a citizen to get by. Mathematical literacy is mathematical knowledge, methods,…
  4. My issues with Understanding by Design (UbD) – Everybody is jumping into this new education bandwagon like it is something that is new indeed. Here are some issues I want to raise about UbD…
  5. Curriculum change and Understanding by Design, what are they solving? – Not many teachers make an issue about curriculum framework or standards in this part of the globe. The only time I remember teachers raised an issue about it was in 1989, when the mathematics curriculum moved …
  6. Math investigation lesson on polygons and algebraic expressions – Understanding is about making connection. The extent to which a concept is understood is a function of the strength of its connection with other concepts. An isolated piece of knowledge is not powerful…
  7. Mathematics is an art – Whether we are conscious of it or not, the way we teach mathematics is very much influenced by what we conceive mathematics is and what is important knowing about it…
  8. Mathematical habits of mind – Learning mathematics is not just about knowing, understanding, and applying its concepts, principles and all the associated mathematical procedures and algorithms. It’s not just even about  acquiring the capacity to solve problem,  to reason, and to communicate…
  9. Subtracting integers using numberline – why it doesn’t help the learning – I have reasons to suspect that for a good percentage of students, the end of their mathematics career begin when they are introduced to subtracting integers. Well, for some, it’s when the x‘s start dropping from the sky without warning…
  10. Teaching positive and negative numbers – Here’s my proposed activity for teaching positive and negative numbers that engages students in higher-level thinking…
  11. Trigonometry – why study triangles – What is so special about triangles? Why did mathematicians created a branch of mathematics devoted to the study of it? Why not quadrinometry? Quadrilaterals, by its variety are far more interesting….
  12. Teaching the concept of function – Mathematics is not just about the study of numbers and shapes but also about the study of patterns and relationships. Function, which can define some of these relationships, is an indispensable tool in its study…
  13. Algebraic thinking and subtracting integers – Part 2 – Algebraic thinking is about recognizing, analyzing, and developing generalizations about patterns in numbers, number operations, and relationships among quantities and their representations.  It doesn’t have to involve working with the x‘s and other stuff of algebra….
  14. Patterns in the tables of integers – Mathematics is said to be the science of patterns. Activities that involve pattern searching is a great way to engage students in mathematical thinking. Here are some of my favorites …
  15. Making generalizations in mathematics – Making generalizations is fundamental to mathematics. Developing the skill of making generalizations and making it part of the students’ mental disposition or  habits of mind …
  16. Teaching with GeoGebra: Squares and Square Roots – This post outlines a teaching sequence for introducing the concept of square roots in a GeoGebra environment. Of course you can do the same activity using grid papers, ruler and calculator….
  17. Algebra vs Arithmetic Thinking – One of the solutions to help students understand algebra in high school is to start the study of algebra earlier hence the elementary school curriculum incorporated some content topics traditionally studied in high school. However,…
  18. Teaching with GeoGebra – Educational technology like GeoGebra can only facilitate understanding if the students themselves use it. This page contains a list of my posts …
  19. Teaching combining algebraic expressions with conceptual understanding – In this post, I will share some ideas on how the simple investigation of drawing polygons with the same area can be used as an introductory lesson to teach operations with algebraic expressions with meaning and understanding.
  20. Mistakes and Misconceptions in Mathematics – Misconceptions are very different from the mistakes students make. Mistakes are not consciously made. Misconceptions are. Mistakes are usually one-off, while misconceptions, the gods forbid, could be for keeps….
Posted in Mathematics education

Why it is bad habit to introduce math concepts through their definitions

In my earlier post on the meaning of understanding, I describe understanding of mathematics as making connections: To understand is to make connections. These connections are not done in random.  Concepts are linked with other concepts in order to create a richer image for the new concept that is being learned. To understand therefore is to form concept image. And a concept image is not formed by defining the concept. The definition of a concept is different from the concept image. Let me share with you a an excerpt from my paper which discusses this idea. You can view the references here.

Understanding the definition does not imply understanding the concept. In order to understand a concept one must have a concept image for it. One’s concept image includes all the non-verbal entities, visual representations, impressions and experiences that are created in our mind by a mention of a concept name (Vinner, 1992). Vinner stressed that the concept definition is not the first thing that is learned in understanding a concept but the experiences associated with it, which becomes part of one’s concept image. Vinner believes that in carrying out cognitive tasks, the mind consults the concept image rather than the concept definition. Continue reading “Why it is bad habit to introduce math concepts through their definitions”