4 Difficulties in Mathematics
Vocabulary
1.Conceptual density of mathematics text- contains more concepts per word, per sentence, or per page than other texts; compounded by lots of abstractions, specialized symbolism, and technical technology.
2.Complex overlap between vocabulary used in mathematics and the vocabulary of everyday language- shared words with different or specialized meanings, for example homonyms.
3.Varied use and large number of mathematics symbols and graphics- more than one word may be needed to verbalize a symbol or set of symbols, symbols are not always read left to right, symbols can have more than one meaning, and ideas expressed in tabular or graphic forms may not easily be expressed in words.
4.Need to understand concepts embedded within other concept- certain concepts are defined and understood only as they are embedded with other concepts, students need to comprehend how concepts fit into larger scheme that includes other related concepts, and vocabulary development activities need to show the relational nature of concepts.
Additional difficulties include:
Vocabulary
1.Conceptual density of mathematics text- contains more concepts per word, per sentence, or per page than other texts; compounded by lots of abstractions, specialized symbolism, and technical technology.
2.Complex overlap between vocabulary used in mathematics and the vocabulary of everyday language- shared words with different or specialized meanings, for example homonyms.
3.Varied use and large number of mathematics symbols and graphics- more than one word may be needed to verbalize a symbol or set of symbols, symbols are not always read left to right, symbols can have more than one meaning, and ideas expressed in tabular or graphic forms may not easily be expressed in words.
4.Need to understand concepts embedded within other concept- certain concepts are defined and understood only as they are embedded with other concepts, students need to comprehend how concepts fit into larger scheme that includes other related concepts, and vocabulary development activities need to show the relational nature of concepts.
Additional difficulties include:
- some mathematical terms are used only in mathematics
- some words have more than one meaning
- some modifiers may change mathematical meanings in important ways
- some mathematical phrases must be learned and understood as a whole
- some words shared with other disciplines have different technical meanings in the two disciplines
- some mathematical concepts are verbalized in more than one way
- students may adopt an informal term as if it is a mathematical term
Building the Language of Mathematics for Students by NC DPI (Vocabulary): Mathematically proficient students communicate precisely by engaging in discussions about their reasoning using appropriate mathematical language. The terms students should learn to use at each grade level with increasing precision are included in this
document.
Foldables by Dinah Zike are an effective tool for student learning; but the benefits of these interactive graphic organizers are certainly not limited to the English language arts. Foldables can also be valuable tools across content areas because they foster the kinds of thinking and writing skills required in all academic learning.
Teaching Mathematics using Dinah Zike Foldables
Explore this video tutorial to view an introduction to Foldables and new products.
Teaching Mathematics using Dinah Zike Foldables
Explore this video tutorial to view an introduction to Foldables and new products.
Research shows that graphic organizers are key to assisting students to improve academic performance.In creating an organizer,pertinent aspects of a concept or topic are arranged into a pattern using labels.This process is one that research suggests aids comprehension for several reasons:
•Graphic organizers match the mind.As researcher David P. Ausubel has shown,the mind arranges and stores information in an orderly fashion.New information about a concept is filed into an existing framework of categories called a schema.A schema already contains preexisting knowledge about that concept.Graphic organizers arrange information in a visual pattern that complements this framework, making information easier to understand and learn. Organizers:
•demonstrate how concepts are linked to prior knowledge to aid in comprehension.
•aid the memory as opposed to recalling key points from an extended text.
•help retain information readily when higher thought processes are involved.
•engage the learner with a combination of the spoken word with printed text and diagrams
Graphic Organizers- Writing can be used to help students connect representations. Enchanted Learning and Teacher Vision have a variety of graphic organizers that help students construct and organize information. A to Z resources and templates.
Four Corners
Number Lines in Common Core
Thinking Maps
Visualizing our thinking allows us to have a concrete image of our abstract thoughts. Visual representations enhance the brain's natural ability to detect and construct meaningful patterns. Thinking Maps reduce anxiety by providing familiar visual patterns for thinking and working with complex ideas and situations.
Visualizing our thinking allows us to have a concrete image of our abstract thoughts. Visual representations enhance the brain's natural ability to detect and construct meaningful patterns. Thinking Maps reduce anxiety by providing familiar visual patterns for thinking and working with complex ideas and situations.