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Creating action schema based on conceptual knowledge

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Baker W., Dias O., Czarnocha B., Soho E.

Didactica Mathematicae

2016

tom 38

Much of constructivist pedagogy focuses on moving past direct instruction or “chalk and talk” to promote active construction of knowledge or teaching for understanding. In this article a group of teacherresearchers conducts two classroom investigations. The first is epistemological (structural) in nature, and the second is functional. In the first investigation, a student’s efforts to employ her conceptual knowledge to guide her actions is analyzed through the lens of a conceptual framework based upon the integration of creativity theory due to Koestler and learning theory due to Piaget. The second investigation focuses on the functional aspect of a teacher’s role in promoting the conceptual based solution activity observed in the first investigation. This functional effort employs visual concepts to direct student actions and is at first ineffective however, later with more transparent structure it is successful. These results suggest student efforts to create action schema and internalize structure through conceptual visuals will depend upon the cognitive gap (ZPD) between the concepts and the coordination involved with the associated actions.

Learning Fractions at a Community College

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Baker W., Czarnocha B., Dias O., Doyle K. M., Prabhu V.

Didactica Mathematicae

2009

tom 32

This paper deals with the process of learning fractions by adult students attending courses of remedial mathematics at community colleges in the Bronx, New York City. It investigates the schema of fractions with the help of the model created by (Charalambos and Pitta-Pantazi, 2007), which is based on the work of Kiernan and the assumption that the fraction schema is composed of five subconstructs, a fundamental part whole subconstruct and four subordinate subconstracts: ratio, quotient, operator and measure. As (Charalambos and Pitta-Pantazi, 2007), conducted their research among young children, its application to the case of adult student brings interesting comparative knowledge about the fraction schema of children and adults.For adult students, we were able to find partial support for the Kiernan fraction schema because all the subordinate sub-constructs except ratio (figure 4, table 3) correlated significantly with the part-whole sub-construct. It was determined that, while the adults engaged in mathematical reasoning about ratios and the abstract operator concept with approximately the same level of proficiency as the children however, the adult students were not able to assimilate this information into their fraction schema nearly as efficiently as the children.It is of significance that adult students had understood ratio as a separate concept from part-whole. The ratio sub-construct is typically used to represent a comparative process between quantities and the part whole sub-construct represents a process of taking a fraction part out of a total.The lack of flexible thinking in understanding the subtle relationship between the fraction as a numerical quantity corresponding to the number of parts taken out of a partitioned whole and as a comparative process in the ratio sub-construct is evidenced by a common addition error. When a students add: 1/3 +2/5 and obtain 3/8 they are incorrectly employing addition of ratios as a natural extension of the addition of whole numbers. The fact that the ratio is separate from the rest of their fraction schema, and that the operation of addition of ratios is a natural extension of whole number addition suggests changes in the curriculum.Perhaps the ratio concept needs to be more extensively taught including its natural operations while highlighting the subtle relationships between the ratio and part-whole sub-constructs.

Ograniczanie wyników

2 Didactica Mathematicae

2 Baker W.

2 Czarnocha B.

2 Dias O.

1 Doyle K. M.

1 Prabhu V.

1 Soho E.

1 2016

1 2009

Wyniki wyszukiwania

Creating action schema based on conceptual knowledge

Learning Fractions at a Community College