Go From Theory to Practice

What are the components of effective mathematics teaching?  What are students doing when they are developing powerful understandings of mathematics?  Be sure to reference course readings in your discussion.

Effective mathematics instruction does not occur by chance or in isolation. It involves the classroom teachers and all other partners in education: parents, school administrations, school boards, specialists, support from the whole community. Each partner plays a significant role by creating the conditions for teachers and students to have the best learning environment possible for the best mathematics program. All partners in education need to know and understand that students perform to the best of their abilities when there is a long-term commitment for their success. 

To teach mathematics right and effectively I can mention few principles that are good habits to the math teacher:

 

1.      Love and live mathematics every day with every pore

2.      Teach the understanding of mathematics more than the right solutions to problems

3.      Remember the goals and prepare the students for life

4.      Know and use the math tools (from the old-fashion abacus, ruler , protractor, compass to the latest technology),

 

The math teacher should know how to create open questions and parallel tasks, making use of the SAMR model that I consider extremely important. The present technology allows for task redesign and creation of new task, as explained by Dr. R. Puentedura.

I think that the math teacher must promote instruction that is unambiguous, and systematic, teaching the key skills in advance in a permanent scaffolding technique.  The math teacher is more productive if his teaching is pivoting on the significant mathematical concepts, the big ideas, in a busy climate of learning.

Researching this topic, I was able to identify some suggestions contributing to the development of math-related abilities in our students.

“General education instruction in mathematics should include: concepts and reasoning (e.g., basic number concepts, meaning of operations such as addition, geometric concepts); automatic recall of number facts (e.g., memorization of basic addition facts such as 3 + 4 so that children know answers instantly instead of having to count); computational algorithms (the written procedure or series of steps for solving more complex types of calculation, e.g., for two-digit addition with regrouping, calculation starts in the right-hand column and tens are "carried" from the ones to the tens column); functional math (e.g., practical applications such as time and money); and verbal problem-solving (e.g., solving word problems)”. (Spear-Swerling, 2005).

This is in fact what the students come to understand when they develop math abilities.

Another strong concept is that students remember learning that makes sense for them and extends their reasoning. They may make use of their memory or not, it is not so important any more.

The conceptual understanding is more important and it is consolidated by inquiry and investigation.

Mathematical investigation is enhanced when students have more time to explore and consolidate mathematical ideas.

Students who understand mathematics are “doing” mathematics by: talking, reflecting, discussing, observing, investigating, listening, and reasoning”. (A Guide to Effective Instruction in Mathematics

Kindergarten to Grade 6).

In the new vision of teaching mathematics, students are encouraged to work together and learn from one another as they demonstrate and communicate their mathematical understanding. Active engagement of students will keep them interested. Building interest and maintaining it by varying methods and by making the topic relevant to the students’ experiences, whenever possible, will make the students see the beauty of math and they may start to love it.

The Guide to Effective Instruction in Mathematics suggests making use of the learning styles preferred by students, according to Gardner’s’ intelligences, including the kinaesthetic, the artistic, or the musical students. I know this seems impossible, but there is always a way to connect concepts for the thinking mind.

The teacher is the one asked to present mathematical concepts in a variety of ways providing students with the opportunity to make connections with the outside environment and their home life.

The familiarity of their specific environment is an advantage we should use in our practice, making mathematics more accessible. As we know mathematical knowledge is abstract and to teach abstract, logical thinking is a facet that produces reluctance and adversity. That is why the connection to real-life events is so important.

A powerful understanding of mathematics needs to be completed by providing constructive feedback to students, determining the next steps,  and keeping all channels of communication open (to parents, community, school boards).

In western countries, such as Canada, there is a much stronger emphasis both on student-centered approaches to mathematics teaching and learning and on the need for the mathematics to be practical and relevant to the learners. Thus effective teachers must understand the students’ needs, be more flexible and engage in less structured lessons.

 

Resources:

A Guide to Effective Instruction in Mathematics K-6

www.edugains.ca/newsite/math/guides_effective_instruction.html

 

Small, M. (2010). Beyond one right answer.  Educational Leadership, 68(1), 28-32. http://search.ebscohost.com.proxy1.lib.uwo.ca/login.aspx?direct=true&db=tfh&AN=53491078&site=e host-live  

Spear-Swerling.L.(2005). Components of Effective Mathematics Instruction http://www.ldonline.org/article/Components_of_Effective_Mathematics_Instruction?theme=print

The SAMR Model Explained by Dr. R. Puentedura. https://www.youtube.com/watch?v=_QOsz4AaZ2k