Cubical Counting Blocks

The Carden®Language of Numbers prepares young people to educate themselves in any occupation involving mathematics. It does so by developing math vocabulary, encouraging mathematical thinking outside the classroom, and assuring math comprehension. Although certain specifics with regard to math may change, ability to communicate in the language of numbers will enable students to grow as knowledge of math unfolds. 

As in Carden® language arts, students are guided by their teachers to first experience, then identify, and finally, define the concept being learned. This procedure assures a firm grasp of mathematical concepts and a strong foundation for the future. 

How is Math presented in a Carden® classroom?

The teacher's first step is to remove vocabulary as an obstacle. He or she makes certain that the student understands the vocabulary being used in the context of mathematics.

This process begins in Carden® preschool, where children learn the vocabulary of arithmetic through the use of colored cubical counting blocks. They learn vocabulary such as lowest, highest, first, second, and third. This vocabulary in the context of mathematics is reinforced during language arts lessons, when, for example, children are asked to identify “the one letter before” or “the second letter after” the one being indicated by the teacher. 

Moving on through elementary school, students are helped to make vocabulary an asset, not a liability. Because of the strong emphasis Carden® places upon reading comprehension, students are able to read and understand a mathematical problem, clearly identifying the operation needed to solve the problem correctly. They are not so intimidated by the language of a word problem that they simply take the two (or three) easily-spotted numbers and add/subtract/divide. They read the problem, comprehend what is needed, and perform the calculation.

The second step begins once vocabulary is in place. Now the Carden® teacher helps his or her students to experience the new math concept being presented. First, the students are given a preview of the total picture. Second, the students are helped to identify main concepts and principles in their relations to each other and to previous work done in class. Third, they begin to relate details to the structure of the whole concept. Background is supplied as necessary to deepen understanding. Next, the students have an opportunity to use the new concept learned through a real-life example. A good Carden® teacher prepares helpful questions along the lines of those provided in detailed Carden® Language of Numbers teacher’s texts.

Teacher texts in the Carden® Language of Numbers series use carefully designed questions that focus attention rather than scattering it. The questions asked as the lesson is taught develop comprehension. The questions asked after the presentation of the concept test comprehension. All questions must have a purpose. What should the student understand? What should the student know? What should the student be able to do after the lesson?

The third step involves reading the math text with the students. The lesson is previewed for the students as the teacher reads the assignment through without interruption so that all can get a general idea of what is required. Next a brief discussion of the key words and titles[1]found in the math text’s instructions. This will yield a brief outline of the overall lesson. Now, examine the lesson. When important ideas are given in the math text, use a question to focus attention on the idea or assign a brief task that will help the students see the point.


[1]Further discussion of Carden® key words and titles can be found in “The Carden® Reading Method.” Briefly, these terms refer to the main idea of a sentence, and then a clarification of the content of the sentence, both tools of reading comprehension. Note that again Carden® language arts and math cross paths because the Carden® curriculum is fully interrelated.