Common sense tells us that reading vocabulary and comprehension are linked. Using word definitions, though, doesn’t work as an instructional approach for improving reading comprehension. Effective vocabulary instruction should include metacognitive reading strategies such as determining the significance of particular words to the overall meaning of the text, assessing prior knowledge about a word and the concept it represents, considering various meanings of a word, relating the significance of a given concept to the subject matter, locating context clues, and recognizing the need for repeated exposures to the target words. You can think about vocabulary acquistion much as you would think about solving problems because word learning and problem solving, it turns out, are similar processes.

Martha Rapp Ruddell recognized four possible approaches to word learning:

  • The aptitude position proposes that we have an innate mental mechanism responsible for general verbal ability;
  • The instrumentalist position emphasizes knowing individual word meanings;
  • The access position includes using context, structural analysis, dictionary definitions, word mapping, mnemonic devices, semantic featural analysis, and semantic mapping;
  • The knowledge position credits background knowledge as the essential element in comprehension. Words, according to this view, represent the tip of the conceptual iceberg since knowing a word implies that one knows many related words and that these words serve as markers for a broad conceptual base.

Ruddell linked these perspectives as a set of complementary elements under the umbrella concept of ‘knowledge.’ Ruddell looked at each of them as characteristic of either declarative, procedural, or conditional knowledge. Additionally, she proposed that the stance of the learner toward the text in which the words are encountered plays a significant part in vocabulary acquisition and assimilation.

Schoenfeld’s model for mathematical problem solving is remarkably similar to Ruddell’s perspectives on vocabulary and comprehension discussed above. Schoenfeld argued that problem solving skill is not necessarily indicative of mathematical understanding since problems can be solved by exploiting superficial procedural knowledge. As a result, in order to better understand effective mathematical thinking, he identified four different types of knowledge and behavior that characterize successful mathematical problem solving performance.

  • Declarative knowledge is an element in problem solving: facts, algorithmic procedures, and informal knowledge about the problem belong to the category of resources.
  • Heuristic knowledge is vital to problem solving since it provides the mathematician with a framework that suggests various approaches which could be taken to reach a solution to a problem. Schoenfeld mentioned the use of heuristic devices such as drawing diagrams, making connections with related problems, and working backwards from the solution. The heuristic knowledge that Schoenfeld sees as a necessary component of mathematical understanding is recognized as procedural knowledge by Ruddell. Schoenfeld recognized that the major limitation of heuristic strategies is their dependence on both background knowledge and decision-making ability.
  • Control is also a factor in successful problem solving . Within this category are what have been generally described as metacognitive strategies. This aspect of problem solving involves planning, monitoring, and the assessment of the problem solving effort itself - including time management. The aptitude perspective on vocabulary knowledge, Ruddell’s conditional knowledge, is similar to Schoenfeld’s control category for effective problem solving behaviors since they both involve resource allocation and executive functions of self-monitoring that determine how a particular performance is evaluated by the individual learner.
  • Belief systems have an effect on an individual’s mathematical performance, according to Schoenfeld, and occupy a “precarious middle ground between primarily cognitive and primarily affective determinants of mathematical behavior” (1985, p. 154). He cited research on the “contextually bound nature of thought processes” in everyday cognition that account for failures to use available knowledge. These accounts of “inadequate model building” (1985, p. 151) in the construction of solutions to problems are examples of beliefs at work on the cognitive level.

Schoenfeld’s belief systems and Ruddell’s reader stance are in close alignment insofar as they recognize that interpretation of problems and unfamiliar words is influenced by the learner’s background and the context in which the problem has been posed.

diagram

The similarities between these two comprehension models is striking. It appears that mathematics and vocabulary comprehension processes are parallel. Meaningful word learning is in many respects a problem which can be approached similar to the way a mathematician solves a problem.

Recognizing that the same dynamics are at work with vocabulary acquisition as with solving mathematics problems indicates that mathematics learning, like language learning, must be linked to meaningful communication and not simply limited to procedural or syntactic manipulations. Vocabulary learning should likewise not depend on simple procedures like looking for dictionary definitions and using new words in sentences. Instead we should include vocabulary learning as part of an overall set of comprehension strategies.

Sources:

Allen, J. (1999). Words, words, words: Teaching vocabulary in grades 4-12. York, Maine: Stenhouse Publishers.

Ruddell, M. R. (1994). Vocabulary knowledge and comprehension: A comprehension-process view of complex literacy relationships. In R. B. Rudell & M. R. Rudell & H. Singer (Eds.), Theoretical models and processes of reading (pp. 414-447). Newark, Delaware: International Reading Association.

Schoenfeld, A. H. (1985). Mathematical Problem Solving. Orlando, Florida: Academic Press, Inc.