Adding Up: Helping Children Learn Mathematics

This was another very interesting reading, about 30 pages. It focuses on the situation of the current teaching and learning math in the US, "weakness in the mathematical performance of the US students". recognizing some of its challenges at a global perspective, recognizing some of the small steps, I would say, of improvement that it has had during the last years, but over all focusing on how to improve the access to mathematics to all students in the classrooms of the US. The inform is based on the reviewing of many of the literature, research and studies that have been made to the date. And it is for teaching Math from K to 8 grade (elementary school only).

They said they choose to focus on the concept and understanding of NUMBER, or how they called also, Numeracy. The focus is on how we, the math teachers, should teach how to think, to interpret math, the logic, the reasoning, more than the mechanical procedure of moving numbers around.

They were based on the understanding of Number, that I interpret like the basic math operations, addition, subtraction, multiplication and division. And how with the understanding of these procedures, in terms of learning the logical behind the operations, our students could be more ready to take the next step of generalization numbers concepts and go into algebra.

According to the article, the US is behind most, or all, the developed countries in the proficiency of the elementary students in math.  And as I mentioned before, they put the emphasis on how to we, the math or class teachers. are teaching math. Touching on the books also, says "cover more topics, but more superficially".

Some of the ideas that called my attention regarding to the lecture are the following:

"All young Americans must learn to think mathematically and they must think mathematically to learn"

And in something that concern to us in the US, says "too few students in our elementary and middle schools are successfully acquiring the mathematical knowledge , the skill, and the confidence they need to use mathematics they have learned.." and in a assertion that I think refers to minorities and special ed students, with out mention them, continues "certain segments of the US population are not well represented among those who do not succeed in school mathematics".

Other interesting quotation "curriculum and the methods used to bring about tat curriculum depend in part on what society wants to be educated adults to know and be able to do....fro example, what knowledge, skills, and abilities employees need in the workplace".

One of the central points of the reading is that they choose "Mathematical Proficiency" to capture what they think it means for anyone to learn mathematics successfully. And it has three strands, that we should live with, are:

1. Conceptual Understanding - comprehension of mathematical concepts, operations, and relations

2. Procedural Fluency - skill in carrying out procedures flexibility, accurately, efficiently, and appropriately

3. Strategic Competence - ability to formulate, represent, and solve mathematical problems.

4. Adaptive Reasoning - capacity for logical thought, reflection, explanation, and justification.

5. Productive Disposition - habitual inclination to see mathematics as sensible, useful, and worhtwhile, coupled with a belief in diligence and one's own efficacy.

Talking about teaching, refers that "The effectiveness of mathematics teaching and learning is a function of teachers' knowledge and use of mathematical content, of teachers' attention to and work with students, and of students' engagement in and use of mathematical tasks. And that we should have "High Expectations" from our students, and I agree with it. How do I am implementing this agreement is something that sometimes I think about.

In the recommendations, they say that "The overriding promise of our work is that throughout the grades from pre-K through 8 all students can and should be mathematically proficient".

And going back to the main point:"significant instruction time is devoted to developing concepts and methods, and carefully directed practice, with feedback".

Also these other ideas,to which they place very specific attention, that by the way, I do know if the schools really apply: "Schools should support, as central part of teachers' work, engagement in sustained efforts to improve their mathematics instruction," providing time and resources. Because, 'improving students' learning depends on the capabilities of the classroom teachers... Learning to teach well cannot be accomplished once and for all in a pre-service program; it is a career-long challenge...The teachers are just as much learners as the students are".

Later the document makes some mention of comparation of the attention given to reading in the schools, saying that the same attention is not given to math, although both are of vital importance in the learning process.

It touches also in the fact that this teaching and learning do not only depends on teachers and students, but also on "policy makers, teacher educators, researchers, administrators, and others.

And finally that, "decisions about how to help students reach learning goals can never be made with absolute certainty"