Error Patterns and Misconceptions in Math
Error Patterns and Misconceptions in Math
Need for Diagnosing Error Patterns
Learning is a personal process. This is personal attributes influence individuals way of learning by influencing how these individuals interpret information (Ashlock, 2006). Sometimes, personal attributes such as culture and personality, may be characterized by misconceptions about a certain field of learning. This may influence the approach of these individuals towards the field of study.
Therefore, teachers have to understand the students’ misconceptions and error patterns in order to design a learning experience that overcomes this misconceptions error. Understanding misconceptions and error patterns will enable teachers to plan instructions that addressing the needs of every student.
How educators can Diagnose Errors
Teacher need to know and understand their students in order to diagnose misconceptions and errors. Teachers can understand their students by observing the students behaviors. Mathematics teachers need to observe their students during class (Ashlock, 2006). The teachers need to observe their students reasoning and approaches while solving mathematical problems. Teachers may also diagnose error patterns by probing key understandings. The teacher may ask students questions in order to evaluate their understanding of mathematical concepts. The teacher may request students to explain mathematical concept.
Teachers may diagnose error patters by assigning tests and tasks. Continuous assessment tests can be significant tools for assessing students understanding of mathematical concepts. The teacher will be able to trace the students’ progress through this assessment test. The tests also assist the educator to understand the student ability and weaknesses. The teacher may also diagnose errors by assigning tasks to students.
The teacher may assign mathematical problems for students to solve. It is paramount for the teacher to ask students to explain the rationale they used to derive solutions rather than emphasizing on the accuracy of the solutions. This will be an effective way of evaluating misconceptions and error patterns among the students.
Main Misconceptions and Error Patters
Misconceptions and error patterns are common in the field of mathematics. One of the common misconceptions that students have is that multiplication must always results in bigger number (Ameida, 2010). This misconception originates from the student preexisting knowledge of multiplying whole number. Multiplying whole numbers usually results in a bigger product.
However, this is usually not the case when multiplying fractions or decimals. However, since students first learn how to multiply whole number first, they tend to assume that multiplication of decimals must also result in a big number. Another common misconception among students involves the transfer of algorithms for multiplying fractions to the process of adding fractions (Ameida, 2010).
Many students often add the fractions directly, without find a common denominator, like in the multiplication process. Inversion misconceptions also take place when students understand that one cannot deduct a large number from a small number (Ameida, 2010). This becomes a problem when the subtraction involves multiple digit numbers. Students often reverse the subtraction when the number above is smaller than the subtracting number instead of borrowing from the next column.
Strategies for Addressing Misconceptions
Misconceptions hinder students from gaining accurate understanding of mathematical concepts (Ryan & McCrae, 2010). Thus, teachers must address these misconceptions in order to promote meaningful learning. Misconceptions are best addressed by understanding the students existing knowledge and the interaction of these students knowledge with new information. Misconceptions often occur when new information interacts with the existing ideas of the students (Ryan & McCrae, 2010). Thus, teachers need to understand the students existing ideas in order to address the misconceptions.
Part II
The student’s work, in the handout “Misconception and Error Patterns’’, contains generalization errors in the regrouping procedures (Begeson, 2000). The students has applied the algorithm for regrouping numbers during addition and applied in a multiplication task. In additional task, students add the vale that needs to be regrouped to the amount in the next column and proceeds with the addition of the number in the next column (Begeson, 2000).
However, this does not apply to the multiplication process. In multiplication tasks, students usually multiply the number in the next column first before adding the value that needs to be regrouped (Begeson, 2000). The student, in this case, has made first adding the value that needs to be regrouped before proceeding with the multiplication procedure. This misconception originates from the students existing knowledge in adding multiple digits numbers.
The students mistakes elaborate that the student lacks adequate understanding of the difference between in addition and multiplications (Harel, 2000). The student has applied concepts used in addition procedure in solving a multiplication problem. This error may originate from the misconception that multiplication is equivalent to continuous addition (Harel, 2000). Many students associate the process of multiplication with continuous addition (Harel, 2010).
As a result, student often apply addition concept while solving multiplication problems. The Teacher needs to explain the difference between addition and subtraction, especially where multiple digits are involved, in order to address this generalization problem. The teacher also needs to design plans that will assist the student to master addition and multiplication procedures. The teacher needs to promote sense making among the students when it comes to addition and subtractions tasks. The teacher needs to promote an advanced way of thinking among the students.
References
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