Show and tell activity (aka lecture method) may work for some but never in a mathematics class. Getting students to explain and ask questions are nice but only when the explanation and the questions are mathematical. Reasoning and justifying are good habits of mind but they are only productive if they are based on mathematical principles. Explaining, asking questions, and substantiating one’s conjecture or generalization make a productive class discussion but they are only productive for learning mathematics if the mathematics is kept in focus. Orchestrating a productive class discussion is by far the most challenging work of mathematics teaching. Stein, Engle, Smith, and Hughes* (https://doi.org/10.1080/10986060802229675) proposed five practices for moving beyond show and tell in teaching mathematics. I have always practiced them in my own teaching whether with students or with teachers and I find them effective especially when the lesson involve cognitively demanding tasks and with multiple solutions. Continue reading “How to orchestrate a mathematically productive class discussion”
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.
Different conceptions of algebra
The kind of task we ask our learners to engage in algebra communicates particular notions of algebra and with it particular use of variable. There are at least four conceptions of algebra embedded in the curriculum. These are reflected in the tasks in textbooks and in our lessons. Zalman Usiskin proposed the following conceptions of algebra in school mathematics. These are present in the curriculum in varying degrees. Continue reading “Different conceptions of algebra”
What is a variable (in mathematics)?
A variable is often talked about in mathematics class as a symbol that stands for numbers. As Prof Zalman Usiskin reminds us, a variable need not only stand for numbers. In Geometry it could stand for a point in Logic, a proposition, in Analysis, a function, in Linear Algebra, a matrix or a vector and even an operation in Higher mathematics. Continue reading “What is a variable (in mathematics)?”
Tips for Teaching Proofs and Proving
I propose here ideas teachers need to know and pay attention to when teaching mathematical proofs and how to prove.
A. What is a (mathematical) proof?
I define proof as a relational network of claims (propositions and conclusions), substantiation (established knowledge that makes the claim legitimate) and appropriate connectives so sequenced to justify why the conclusion is a logical consequence of the premises. Continue reading “Tips for Teaching Proofs and Proving”