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"

 

Help All Students Succeed in Mathematics

This almost 30 pages reading it was very interesting and at the same time, like some others readings, very wide, and therefore, difficult for me to decide from where to attack it, I mean, to consider it, to write about it.

It covers a wide perspective of possibilities on how to work with different kind of students, mainly with students with learning differences, although also takes a small section of working with gifted students, which are, kind of, the two ends of the students spectrum a teacher can find in the classroom. And all is focused on math teaching.

Although, I am not sure about the validity of this previous statement -that is completely mine, about the ends of the spectrum. But the article talks about different types of student with special needs (can we say that?), and then gives some advice and, in some cases, more specific examples of how to work and help these students.

The article starts with some statements of a certain student that is critic and is still frustrated with the type of mathematics education he received. He is now a freshman in college, and he is 21 y.o.

The article goes on how these days, "the emphasis in mathematics instruction should be on problem solving and activity-based learning... The goal is to increase the emphasis on teaching students to solve problems effectively".

Under the aspect of Difficult in Learning Mathematics, it mentions that, according to Kosc (1981), there are four kind of factors that influence the mathematics ability of all students:

 a. Cognitive factors

b. Educational factors

c. Personality factors, and

d. Neuropsychological patterns.

The reading also mentions that "for many students mathematics are heritable".

And talking about problems associated with non verbal math abilities, considers these other factors:

- Social immaturity

- Disorientation

- Deficit in visual, motor, and self-help skills

- Problems estimating distance and time.

One of the main statements of the article refers that "students can display poor math performance for several reasons", and states that "the one that can be most readily corrected is the inadequate instruction in mathematics that many students receive".

Then the reading goes on with extensive recommendations on how to improve ones teaching: assessments, setting expectations, peer tutoring, being a model in math, curriculum based measurement, 'student goal setting and self-monitoring', varied practice, motivation, using games and manipulatives, teaching to estimate, familiar subject matter, etc., focusing especially in how to incorporate, reach and help the success of students with special needs.

And as I said at the beginning, it is inspirational, and at the same time a little overwhelming.

Thank you. 

Helping

Relations, Power of Our Words and Reaching the Fragile

It pretends to be an encompassing posting on these three readings: Relationships Matter (Deborah Stipek, School of Education's Dean, Stanford University, 2006), The Power of Our Words (Paula Denton, Northeast Foundation for Children, 2008), and Reaching the Fragile Student (Sue Zapf, Compass Program, Minnesota, 2008).

These articles focus on the relation between teacher and students, on three different but interrelated aspects: The first one on general good relations between the teacher and the students, emphasizing nurturing, supporting relations; the second one how language should be used to positively shape learners; and the third one on how to reach and help to succeed the 'fragile' student.

And we are talking here on a recurrent but not for that easy nor simple subject on education and in REACH: How we teachers, and the schools in which we teach, can create an environment in our classrooms where the relation between teacher and student goes well beyond the simple transmission of knowledge, to a much closer, understanding, supporting and caring relation, as expressed on the subtitle of the article, "The key to achievement is connecting students with teachers who support them not just as learners, but also as people".

And this is not as easy road. We talk about it. We know is good for us, as community, as country, as persons, and overall, is good for our students, the new generations, etc., but to translate it to a daily life activity, considering how some of us feel already, overwhelmed with the current level of work and involvement we have, it is the great challenge. 

And I do not want to say that this is not possible to achieve it, but requires a constant effort, a permanent activity of reaching the level of personal, caring and involving relation with our students, until start feeling that our efforts are being fruitful and then you see that it is rewarding.

In my personal experience I would say that, immerse into the field of education in the US these last 8 years in high and middle school, I being doing more and more conscientious effort to reach more and more students and trying to be an element of support in their learning process. But how I said initially, it is easier to talk about it than do it.

As it says in part of the reading "Teachers need to make special efforts to show a personal interest in and interact positively with students whom they find most difficult to teach -by going out of their way compliment positive behaviors, showing an interest in the students' lives outside school, listening to the students' perspectives on the problems they are having, and collaborating with them on developing strategies to address these problems".

And that "The most difficult-to-reach students will often go all out for a teacher who demonstrates caring for them as individuals and commitment to their success".

The power of our words or how do we use language in class, "what do we say and how do we say it", has a profound impact in our students, according to the article. The language we use should be encouraging, with recognition and prizing -academically, listening and understanding. It gives us five guiding principles for positive language:

1. Be direct

2. Convey faith in students' abilities and intentions

3. Focus on actions not abstractions

4. Keep it brief

5. Know when to be silent.

Reaching the fragile student article, talk to us about creating an "inviting" environment for many students that have "failed" in other schools, talk to us about "proactively cultivate 'intentionally inviting' practices that welcome all students into the culture of learning". And keep this attitude until you see the signs of success.

All and all, again, excellent and beautiful expressions, experiences, but not easy to achieve. We are all in this process and hopefully we will use the techniques in the best way we think will benefit our goals of success for our students.

 

Understanding the Symptoms

I am sorry, I tried to post my comments on this reading, pasting it from a word document, but it did not come through. If I have time later, I will try to rewrite it and re-posted it.

I am placing soon a new posting on the new series of readings.

First few weeks

1 ) My first two weeks have been a mix of enthusiasm, over-stretching, tension, hope and learning.

In the middle of all this, the high would be that I have already got, I think, a good respond and connection with two of four of my classes, that I fell very comfortable working with. Those are my largest class, Algebra 1, second period, and my last class, Pre-Algebra, the sixth period. It has been based most on the teaching staff with the first class and on the personal connection with the second one.

2) Things going well: I have been present on all my classes. 1) I been trying to  inspire a professional and confident presence in class. 2) I have been trying to promote work, concentration and collaboration also. 

3)  Area of growth in classroom management, I would say two. One is to gain more solid knowledge and manipulation of subject matter (after so many years of not teaching math) together with more proper planning. And the second is how to reach to shy, challenging and unengaged students.