I don’t get it! I don’t get it! I don’t get it! I got it!!!
or
“Learning Differences” and Problems Achieving Success in Mathematics
Richard C. Gacka Ed.D.
Director, PA Learning Differences Center
Factors other than mathematical reasoning or comprehension frequently are at the root of “wrong
answers.” The following may be some of those factors.
Individuals who display difficulty understanding or complex grammatical patterns.
 Lack of understanding of the sequence or relationship of parts of a sentence.
 Difficulty remembering component parts of a sentence.
 Lack of understanding of grammatical relationships.
 Lack of understanding quantitative or process vocabulary.
o Lack of knowledge of, or inability to translate, “technical” terms.
o Lack of knowledge of core terms that underlie mathematical concepts.
o Substitution of term meanings.
 Inability to sort important from unimportant details.
 Inability to hold information in working memory.
 Inability to perform simultaneous processing.
 Inability to “visualize” what is heard.
 Inadequate “depth” of reasoning, superficial effort.
 Inability to “re-verbalize,” “paraphrase,” or “chunk” what is heard.
Individuals who have difficulty explaining how they arrived at a solution.
 Inability to recall specific terms that define processes.
 Inability to sequence mentally or see critical relationships.
 Inability to formulate correct grammatical sentences.
Individuals do not understand or recall the sequence of actions that led to a solution.
 Lack of knowledge of basic terms that underlie mathematical concepts.
 Difficulty with temporal sequencing.
 Difficulty recognizing “cause-effect” relationships.
Inability to understand “word problems.”
 Poor comprehension of sentence meaning.
 Failure to note critical mathematical terminology.
 Inability to “translate” word problems to numerical representation.
 Inability to hold information in working memory.
 Difficulty in establishing a “plan” for a solution.
 Poor reading comprehension.
 Emotional blocking.
 Inability to translate written to oral/mental word problems.
Poor mastery of basic mathematical facts.
 Unreliable long term memory.
 Number reversals.
 Lack of “back up” recall systems.
 Poor estimation skills.
 Poor attention to details.
“Careless” Errors
 Visual, spatial, or organizational confusion.
 Poor handwriting
 Poor planning – use of resources
 Errors or writing of digits – number formation, transformations
 Lack of self-checking
 Impulsiveness – excessive speed
 Poor estimation skills
 Lack of a system for checking responses.
 Confusion in identifying process signs
 Poor “pacing” or planning of time
 Failure to recognize patterns
 Failure to identify the importance of processes, i.e. lining up numerals
Poor attention or sustained concentration
 Derives no reinforcement from the activity
 Fatigue secondary to concentration
 Loss of interest with multiple items
 Weak self-discipline or perseverance. “Close Enough” phenomenon
 Thinking “ahead” resulting in ignoring key details.
Other factors external to the student that might be reviewed.
 Instructional Content
o Unnecessary complication of presenting problem
 Content / vocabulary
 Grammatical style of author
 Readability level of material
 Mastery of material by instructor
 Speed of material coverage
 Opportunity for multi-sensory or “hands-on” exposure
 Type of feedback given to student
 Intensity of instructional contact
o Contacts scheduled
o Contacts attended
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