Programs should enable all children to:

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

This can be demonstrated by the children in the following ways:

• pose questions and gather data about themselves and their surroundings;
• sort and classify objects according to their attributes and organize data about the objects;
• represent data using concrete objects, pictures, and graphs.

And…programs should enable all children to:

Select and use appropriate statistical methods to analyze data…

This can be demonstrated by the children in the following ways:

• describe parts of the data and the set of data as a whole to determine what the data show.

Sorting and classifying is something we do all the time with children.  We can have children sort nearly anything that we have many of.  It is easier for children to sort by one attribute at a time (for children under 4, only sort by one attribute at a time).  When putting the cutlery out for lunch, put it out in a pile, all mixed up with spoons, forks, and knives.  Have the children sort them before setting the table. There is a great lesson about this very idea in the Early Math Counts site.  Click here to see it.

There are a couple other lessons available in the Early Math Counts site about sorting and classifying.  Click here or here to check them out.

If you try any of them out, let us know how they go.

This lesson is pretty interesting.  It is about “counting back.”  It says that it is for Prek-2nd, but I think it is pretty complex for most 4 year olds.  You might have some children who would benefit from a lesson like this.  Check it out.

According to its website:

The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.

There are six principles that guide their work.

The first is the Equity Principle.  It describes the need for equity in math education for all children.  It demands that all children have access to high-quality math education, with high expectations for all learners.  It also requires that accommodations are made for learning differences and that all classrooms and students are given the resources and supports they need to be successful.

I don’t know about you, but I think the Equity Principle should be the guiding principle for all education, not just math.  Imagine a world where the above ideals are played out in every classroom, in every town, in every age group, all over the world.

Yep- the Equity Principle is cool.

Excellence in mathematics education requires equally high expectations and strong support for all students.

Curriculum:

A curriculum is more than a collection of activities; it must be coherent, focused on important mathematics, and well articulated across the grades.

Teaching:

Effective mathematics teaching requires understanding of what students know and need to learn and then challenging and supporting them to learn it well.

Learning:

Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.

Assessment:

Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

Technology:

Technology is essential to teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.

• Two large right triangles

• One medium-sized right triangle

• Two small right triangles

• One small square

• One parallelogram

According to Gwen Dewar, PhD. in Parenting Science (2009)

Arranged correctly, the shapes can be fitted together as a large square, rectangle, or triangle. They can also be arranged in a variety of complex shapes, including fanciful ones (like the rabbit illustrated here).

There are many ways to play with tangrams. The simplest way is to let kids create their own complex shapes. But traditionally, tangrams are treated as puzzles. The player is shown a target shape (in outline, or silhouette only) and then asked to recreate that shape using the seven pieces.

As noted below, tangrams can also be used to teach kids to measure area without formulas—an approach that should help kids develop an intuitive sense of geometry.

The National Council of Teachers of Mathematics also says of that while children play with Tangrams, they;

• develop positive feelings about geometry

• classify shapes

• develop an intuitive feeling for shapes and geometric    relationships

• develop spatial rotation skills

• develop precise vocabulary for manipulating shapes (e.g., “flip,” “rotate”)

• learn the meaning of “congruent”

 

Try and get a set of these wonderful manipulatives for your center or classroom.  This website has sets of them for larger groups of children.

These 5 content standards are: Numbers and Operations, Algebra, Geometry, Measurement, Data Analysis and Probability.  Over the next few months we are going to talk about each of these in detail (YEAH!).

For now, I want to share the NCTM Statement of Beliefs about math education and children.  This is love!

Statement of Beliefs

As the primary professional organization for teachers of mathematics in grades pre-K–12, the National Council of Teachers of Mathematics (NCTM) has the responsibility to provide broad national leadership in matters related to mathematics education.

In meeting this responsibility, NCTM has developed a set of standards for school mathematics that address content, teaching, and assessment. These standards are guidelines for teachers, schools, districts, states, and provinces to use in planning, implementing, and evaluating high-quality mathematics programs for prekindergarten through grade 12.

The NCTM Standards are based on a set of core beliefs about students, teaching, learning, and mathematics.

We believe the following:

• Every student deserves an excellent program of instruction in mathematics that challenges each student to achieve at the high level required for productive citizenship and employment.
• Every student must be taught by qualified teachers who have a sound knowledge of mathematics and how children learn mathematics and who also hold high expectations for themselves and their students.
• Each school district must develop a complete and coherent mathematics curriculum that focuses, at every grade level, on the development of numerical, algebraic, geometric, and statistical concepts and skills that enable all students to formulate, analyze, and solve problems proficiently. Teachers at every grade level should understand how the mathematics they teach fits into the development of these strands.
• Computational skills and number concepts are essential components of the mathematics curriculum, and a knowledge of estimation and mental computation are more important than ever. By the end of the middle grades, students should have a solid foundation in number, algebra, geometry, measurement, and statistics.
• Teachers guide the learning process in their classrooms and manage the classroom environment through a variety of instructional approaches directly tied to the mathematics content and to students’ needs.
• Learning mathematics is maximized when teachers focus on mathematical thinking and reasoning. Progressively more formal reasoning and mathematical proof should be integrated into the mathematics program as a student continues in school.
• Learning mathematics is enhanced when content is placed in context and is connected to other subject areas and when students are given multiple opportunities to apply mathematics in meaningful ways as part of the learning process.
• The widespread impact of technology on nearly every aspect of our lives requires changes in the content and nature of school mathematics programs. In keeping with these changes, students should be able to use calculators and computers to investigate mathematical concepts and increase their mathematical understanding.
• Students use diverse strategies and different algorithms to solve problems, and teachers must recognize and take advantage of these alternative approaches to help students develop a better understanding of mathematics.
• The assessment of mathematical understanding must be aligned with the content taught and must incorporate multiple sources of information, including standardized tests, quizzes, observations, performance tasks, and mathematical investigations.
• The improvement of mathematics teaching and learning should be guided by ongoing research and by ongoing assessment of school mathematics programs.

Changing mathematics programs in ways that reflect these beliefs requires collaborative efforts and ongoing discussions among all the stakeholders in the process. NCTM stands ready to work with all those who care about improving mathematics education for all students. Through such dialogue and cooperative efforts, we can improve the mathematical competence of the students in mathematics classes across the continent.