Background
We invited five different students to take up the assignments, and out of the five students, we met three physically while two virtually. The participant’s identities remained unanimous and were labeled as participants 1-5. The students were ages 14 years and above and were neither currently enrolled nor had taken any MA 105 course at Chaminade university. The students were required to solve three different mathematical problems and explain their observations and methodologies before arriving at the final answers.
Reflecting Division Task
The first problem in this project involved a division task, and the students were required to solve it: 4581÷7. The first student multiplied seven by 654 and added 3 to get 4581. The student seemed correct since when the quotient was later multiplied by the initial figures, the answer produced was similar to the question set (Usikhen). However, the second student divided the figure in the bracket by 7, sorted them into pairs, divided 45 by 7 to get six and the remainder of 3, and divided 38 with 7 to get five and the remainder of 3.
However, in the third case, the student seemed to have estimated the quotient to derive the final solution (Spaul). The student interestingly did not apply the critical skills of division, and therefore the workings seemed to have involved much guessing. The fourth student divided 4581 by seven and later left the workings in decimal, almost approximating the final answer when left in fraction (Schoenfeld). The last student performed the entire computation using a decimal tree to calculate the quotients (Sfard). The student systematically explained the methods used in deriving the final answer comfortably.
Reflecting the Double Division Task
In the next assignment, the participants were asked to solve 0÷9 and 9÷0 and explain the methodology used to find the problem’s final answer. While working on this task, participant 1 found out that there was no figure left when zero was divided by the whole number (Spaull). However, the second student noted that when zero was divided by 9, it was the same as nine divided by zero; finally, there was an infinitive figure.
However, participants three and four noted that there was no solution to this task since, in each case, the figures were indivisible (Taylor, Van Der Berg, and Mabogoane). However, the last participant tried using a technique in dividing the first part and proved that the answer was zero since a zero divided by any number would generate zero as the final answer.
Reflecting the Fraction Task
The question involved narrating the methodology used in deriving the final answer when ¾ was divided by ½. The first participant started calculations by multiplying the reciprocal of ½ and then cross-canceled it to ¾ to derive the final answer (Thijs and Van den Akker). In the second case, participant two divided the results against each other to get the final quotient which he then simplified. However, the third participant multiplied the figures against the reciprocal of each other and found out the final answer to be whole number and decimal (Thompson). The last two participants seemed to know about carrying out this task as required from the assignment.
General Comparison
The students showed demonstrated variations in their methodologies as each could give a different view of how they performed each task. We encountered similarities in methods used in little circumstances as some of their patterns could easily be detected (Usiskin). In general, the correct methods were used by three students while two students applied different techniques, which could require deep understanding in their application (Usikhen). In summary, the students attempted the three tasks on average as there was little difficulty in carrying out computations. The students ended up with almost correct answers regardless of the methodologies used.
Works Cited
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