The+Proficiency+Strands

=The Proficiency Strands : Understanding, Fluency, Problem Solving and Reasoning=

The ACM is much more than just content strands. In trying to incorporate what mathematicians actually //do//, the ACM includes the **proficiency strands:** understanding, fluency, problem solving and reasoning.

From the ACM: ACM Description of Content and Proficiency Strands

//The proficiency strands describe the actions in which students can engage when learning and using the content. While not all proficiency strands apply to every content description, they indicate the breadth of mathematical actions that teachers can emphasise .// It is worth carefully reading the description of the last two proficiency strands: //Problem Solving//

//Students develop the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. Students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.//

//Reasoning//

//Students develop an increasingly sophisticated capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false and when they compare and contrast related ideas and explain their choices.//

Peter Sullivan's 2011 ACER report Chapter 2 "The goals of school mathematics" contains an excellent description of the proficiencies and their role in mathematics education.

When you are designing your program, **how much time are you making for Problem Solving and Reasoning**? Here is some food for thought from Charles Lovitt and Doug Clarke. //Full size posters available in the source article.//
 * [[image:http://www.educationaldesigner.org/ed/volume1/issue4/article15/images/fig2_large.png width="270" height="160" caption="Being a mathematician" link="@http://www.educationaldesigner.org/ed/volume1/issue4/article15/"]] || [[image:http://www.educationaldesigner.org/ed/volume1/issue4/article15/images/fig3_large.png width="270" height="160" caption="Problem Solving Strategies" link="@http://www.educationaldesigner.org/ed/volume1/issue4/article15/"]] ||