Tag: mathematical literacy

Posted in Curriculum Reform

What is mathematical literacy?

Posted on by
Defining mathematical literacy

The Program for International Student Assessment (PISA) of the OECD describes mathematical literacy as:

“an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgments and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen” (OECD,1999).

Mathematical literacy therefore 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, and processes applied in various contexts in insightful and reflective ways. According to de Lange, mathematical literacy is the overarching literacy that includes numeracy, quantitative literacy and spatial literacy. Each of these type of literacy empowers the individual in making sense of and understanding aspects of the world and his/her experiences.

De Lange’s tree structure of mathematical literacy.Spatial literacy empowers an individual to understand the three-dimensional world in which he/she lives and move. This necessitates understanding of properties of objects, the relative positions of objects and its effect on one’s visual perception, the creation of all kinds of three-dimensional paths and routes, navigational practices, etc. Numeracy is the ability to handle numbers and data in order to evaluate statements regarding problems and situations that needs mental processing and estimating real-world context. Quantitative literacy expands numeracy to include use of mathematics in dealing with change, quantitative relationships and uncertainties. Click here for deLange’s paper on this topic.

Implications to curriculum and instruction

To identify and understand the role that mathematics plays in the world is to be literate about mathematics and its applications. This means that individuals need to have an understanding of its core concepts, tools of inquiry, methods and structure.

To be able use mathematics in ways that meet the needs of one’s life as a constructive, concerned, and reflective citizen necessitates learning mathematics that is not isolated from the students’ experiences.

To be able to use mathematics to make well-founded judgment demands learning experiences that would engage students in problem solving and investigation as these would equip them to use mathematics to represent, communicate, and reason, to make decisions and to participate creatively and productively in the functioning of society.

These show that mathematical literacy requires learning mathematical concepts and principles that would be applicable to the individual and society’s life and activities; equip individuals the necessary skills in using mathematics to reason and make decisions; enable individuals to get a sense of the nature and power of the discipline in order to understand its role in the world.

To teach mathematical literacy, curriculum and instruction should therefore include these 3 R’s:

  • Relevant mathematical concepts, principles and procedures
  • Real-life context which can be investigated and modeled mathematically
  • Rich mathematical tasks that fosters conceptual understanding and development of skills and habits of mind

Check out these great books on mathematical literacy:

Posted in Curriculum Reform

Mathematical habits of mind

Posted on by

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. It is about making these capacities part of students’ thinking habits. It is only then that one can be said to be mathematically literate.

The test for example that solving problem is no longer just a skill but has become part of students thinking habit is when students are doing it without the teachers still having to ask “Can you explain why you solve it that way?” or “Can you do it another way?” Those should be automatic to students.

“A habit is any activity that is so well established that it occurs without thought on the part of the individual.”

Here’s is a list of important mathematical habits of mind that I believe every teacher should aim for in any mathematics lesson.

Habit #1: Searching for Patterns

Students should develop the habit of

  • generating cases and generalizing patterns
  • looking-out for short-cuts that arise from patterns in calculations
  • investigating special cases, extreme cases from patterns observed

Habit #2: Reasoning

Students should develop the habit of

  • explaining the positions they take
  • providing mathematical evidence/justification for the conjectures or generalizations they make
  • testing conjectures by generating cases both special and extreme
  • justifying why a generalization will work for all cases or for some cases only

Habit #3: Solving and posing problems

Students should develop the habit of

  • always looking for alternative solutions to problems
  • extending problems and solutions to more general case
  • solving problems algebraically, geometrically, numerically
  • asking clarifying and extending questions

Habit # 4: Making connections

Students should develop the habit of

  • Linking algebra, number, geometry, statistics and probability
  • Finding/devising equivalent representations of the same concept
  • Linking math concepts to real-world situation

Habit #5: Communicating mathematically

Students should develop the habit of

  • using appropriate notation and representation
  • noticing faulty, incomplete or misleading use of numbers

Habit #6: Reflecting and self-directing learning

Habit is a cable

All these are only possible  in an environment where students are engage in problem solving and mathematical investigation tasks.

If you want to know more about mathematical thinking, the books below are great read.