ATTENTION:
BEFORE YOU READ THE ABSTRACT OR CHAPTER ONE OF THE PROJECT TOPIC BELOW, PLEASE READ THE INFORMATION BELOW.THANK YOU!
INFORMATION:
YOU CAN GET THE COMPLETE PROJECT OF THE TOPIC BELOW. THE FULL PROJECT COSTS N5,000 ONLY. THE FULL INFORMATION ON HOW TO PAY AND GET THE COMPLETE PROJECT IS AT THE BOTTOM OF THIS PAGE. OR YOU CAN CALL: 08068231953, 08168759420
WHATSAPP US ON 08137701720
ORCHESTRATING SEMIOTIC LEAPS FROM TACIT TO CULTURAL QUANTITATIVE REASONING—THE CASE OF ANTICIPATING EXPERIMENTAL OUTCOMES OF A QUASI-BINOMIAL RANDOM GENERATOR
This article reports on a case study from a design-based research project that investigated how students make sense of the disciplinary tools they are taught to use, and specifically, what personal, interpersonal, and material resources support this process. The probability topic of binomial distribution was selected due to robust documentation of widespread student error in comparing likelihoods of possible events generated in random compound-event experiments, such as flipping a coin four times, for example, students erroneously evaluate HHHT as more likely than HHHH, whereas in fact these are 2 of 16 equiprobable elemental events in the sample space of this experiment. The study’s conjecture was that students’ intuitive reasoning underlying these canonical errors is nevertheless in accordance with mathematical theory: student intuition is couched in terms of an unexpanded sample space—that is, five heteroprobable aggregate events (no-H, 1H, 2H, 3H, 4H), and therefore students’ judgments should be understood accordingly as correct, for example, the combination “3H, 1T” is indeed more likely than “4H,” because “3H, 1T” can occur in four different orders (HHHT, HHTH, HTHH, THHH) but “4H” has only a single permutation (HHHH). The design problem was how to help students reconcile their mathematically correct 5 aggregate-event intuition with the expanded 16 elemental-event sample space. A sequence of activities was designed involving estimation of the outcome distribution in an urn-type quasi-binomial sampling experiment, followed by the construction and interpretation of its expanded sample space. Li, whose experiences were typical of a total of twenty-eight Grade 4–6 participants in individual semi-structured clinical interviews, successfully built on his population-to-sample expectation of likelihood in developing the notion of the expanded sample space. Drawing on cognitive-science, sociocultural, and cultural-semiotics theories of mathematical learning, I develop the construct semiotic leap to account for how Li appropriated as a warrant for his intuitive inference an artifact that had initially made no sense to him. More broadly, I conclude that students can ground mathematical procedures they are taught to operate even when they initially do not understand the rationale or objective of these cultural artifacts (i.e., students who are taught a procedure can still be guided to re-invent the procedure-as-instrument).
HOW TO RECEIVE PROJECT MATERIAL(S)
After paying the appropriate amount (#5,000) into our bank Account below, send the following information to
08068231953 or 08168759420
(1) Your project topics
(2) Email Address
(3) Payment Name
(4) Teller Number
We will send your material(s) after we receive bank alert
BANK ACCOUNTS
Account Name: AMUTAH DANIEL CHUKWUDI
Account Number: 0046579864
Bank: GTBank.
OR
Account Name: AMUTAH DANIEL CHUKWUDI
Account Number: 3139283609
Bank: FIRST BANK
FOR MORE INFORMATION, CALL:
08068231953 or 08168759420