PREPARING PRESERVICE TEACHERS TO TEACH PROBABILITY USING HEURISTICS
PREPARING PRE-SERVICE TEACHERS TO TEACH PROBABILITY USING HEURISTICS By Sweet Rose P. Leonares Presented by Sweet Rose P. Leonares University of St. La Salle Bacolod City 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
INTRODUCTION The study of probability is important… Ø Influences individual and collective decisions made concerning everyday activities According to studies: Ø In-service teachers do not have adequate understanding and training (Batanero & Diaz, 2012; Batanero, Godino & Roa, 2004) Ø Teacher education programs do not provide adequate training for the teaching of probability (Reston, 2012) Ø Therefore: instill both in- and pre-service teachers its importance and identify more effective teaching strategies 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
OBJECTIVES This study aimed to determine if there was improvement in the 1. level of performance, 2. extent of heuristics use, and 3. levels of error when pre-service teachers solved probability problems before and after instruction. 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
THEORETICAL and CONCEPTUAL UNDERPINNINGS • Enactivist theory of learning • Vygotsky’s Zone of Proximal Development • Outcomes-based Teaching and Learning • Heuristics • Newman’s Error Analysis 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
METHODOLOGY • Research design: descriptive qualitative method using the phenomenographic approach • Participants: • Instruments: • Data analysis: 15 third year Bachelor of Secondary Education (Mathematics) students of an HEI in Bacolod City who were enrolled in Probability Theory for the first semester, AY 2015 -2016 * teacher-made or modified Pretest and Posttest on probability problem solving * Newman Error Analysis prompts and rubric * identification of heuristics used * determining and comparing the error profiles 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
SUMMARY OF RESULTS A. Items correctly answered Number of students 16 14 12 10 8 6 4 2 0 1 4 a 4 b 2 3 Item number Pretest 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City 5 6 Post test E. Student Improvement in scores
B. Heuristics use 45 40 Frequency of use (multiple response) 35 30 25 20 15 10 5 0 1 4 a 4 b 2 3 5 6 1 4 a pretest Representation 4 b 2 posttest Simplification 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City Generic None 3 5 6
C. Examples of heuristics use (pretest / posttest – same student) 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
D. Error Analysis Number fo students 16 14 12 10 8 6 4 2 0 1 4 a 4 b 2 3 5 Pretest Items Reading Encoding Comprehension No Error 6 1 4 a 4 b 2 3 5 6 Posttest Items Transformation Careless Error (X) Process Comparison of Errors Committed between the Pretest and Posttest, by item 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City SUMMARY OF RESULTS
E. Student Improvement in scores Number of Items with correct solutions 6 5 4 3 2 1 La ni e Be ck y H ei di H el en Ja ck ie M ila Li n G a le nd C a ha ris Em ilie Jo ni e Ka ira a Ed n ne Ja Su sa n 0 Pre-servce teacher's name pretest 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City posttest
Conclusions and Recommendations Conclusions • Pre-service teachers had very little knowledge of probability at the beginning of the semester but showed marked increase in the number of correct answers in the posttest • There seems to be difficulty in understanding probability of dependent or sequential events • Heuristics use was limited in the pretest but there was substantial and intentional use in the posttest Recommendations • Increase the number of units for probability • Intentional use of heuristics in teaching probability • Future studies on the use of other pedagogical methods 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Thank you! 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
PRETEST AND POSTTEST PROBLEMS PRETEST POSTTEST 1. In a class about Asian A school surveyed the Civilizations there are 35 students, favorite snacks of 1000 of of which 10 are males. The its students. Of the 625 teacher of this class has prepared male students who were class cards, one for every student. surveyed, 200 liked ice Every meeting the teacher cream, 125 preferred pizza, conducts a graded oral recitation while 300 chose hamburger. concerning the topic assigned for Among those surveyed, the day. In order to determine who 300 liked ice cream, and is going to recite, he shuffles the 450 chose hamburgers. A class cards and randomly selects student is selected at one. What is the probability that random from the group. for a particular question, a female Find the probability that the student will have to answer? student is not male. 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
PRETEST POSTTEST 2. The probability that a person The probability that a student vacationing in Bacolod will attending a certain college in visit Mambukal is 0. 33 and Cebu will purchase a laptop is that he will visit the Ruins is 13/20. The probability that he 0. 92. His decision to visit one will buy an MP 4 player is 3/10. site is not affected by his If buying an MP 4 is not decision to visit the other. influenced by whether he What is the probability that a bought a laptop or not, what is person vacationing here will the probability that he will buy visit both sites? the laptop and the MP 4? 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
PRETEST POSTTEST 3. Twenty percent of the A geology professor has two students in a chemistry graduate assistants helping with class are physics majors, her research, one younger (A) sixty percent are chemistry than the other. The probability majors, and twelve percent that the older (B) of the two will of them are majoring in both be absent on any given day is chemistry and physics. 0. 08; the probability that the What is the probability that younger of the two will be a randomly chosen student absent on any given day is 0. 06; will be a chemistry major or and the probability that both will physics major (or both)? be absent on any given day is 0. 02. Find the probability that either of the two assistants is absent. 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
PRETEST POSTTEST 4. Darlene has four suitors: Miko anticipates that she will be Andoy, Bugoy, Caloy, and exempted from taking the final Dodoy. According to her, exams in some subjects. She Bugoy has twice thinks that she has three times as the chances of Andoy and many chances of being exempted in Caloy, while Dodoy has three Linear Algebra as Probability times the chances of Bugoy of Theory, five times as many chances becoming her of being exempted in Filipino as boyfriend. Only one of these Probability theory, and twice as suitors will eventually become many chances of being exempted in her boyfriend. What is the Probability Theory as Assessment. probability that Darlene’s Find the probability that Miko will be boyfriend will exempted from taking the final exam a. be Bugoy? in b. either be Dodoy or a. Filipino. Caloy? b. any Math subject. 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
PRETEST 5. A class in advanced physics is composed of 15 juniors, 30 seniors, and 5 graduate students. The final grades showed that 7 of the juniors, 12 of the seniors, and 3 of the graduate students received a 1. 5 for the course. If a student is selected at random, find the probability that the student is a senior, if it is known that he/she got a grade of 1. 5 (adapted from Walpole, 1982). 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City POSTTEST A school surveyed the favorite snacks of 1000 of its students. Of the 625 male students who were surveyed, 200 liked ice cream, 125 preferred pizza, while 300 chose hamburger. Among those surveyed, 300 liked ice cream, and 450 chose hamburgers. A student is selected at random from the group. If it is known that the student is female, find the probability that she likes pizza.
PRETEST POSTTEST 6. Find the probability of 1. In a class about Asian randomly selecting two Civilizations there are 35 students, good tetrapaks of milk of which 10 are males. The in succession from a teacher of this class has prepared cooler containing 20 class cards, one for every student. tetrapaks of which 5 Every meeting the teacher have spoiled. conducts a graded oral recitation concerning the topic assigned for (adapted from the day. In order to determine who Walpole, 1982) is going to recite, he shuffles the class cards and randomly selects one. What is the probability that for two successive questions, two male students are called to answer one question each? 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Newman Error Analysis Prompts and Rubric Type of Code Error R Reading Prompt Explanation Could not read a key word or symbol in the written “Read the problem to the extent that question to me. this prevented him/her from If you don’t know proceeding further along an a word, tell me. ” appropriate problem-solving path 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Code Type of Error C Prompt Explanation Able to read all the words in the question, but has “Tell me what not grasped the overall the question meaning of the words Comprehension asked you to and, therefore, was do. ” unable to proceed further along an appropriate problem-solving path 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Code Type of Error T Prompt Explanation Had understood what the “Now tell me questions wanted him/her what method to find out but was unable Transformation you used to to identify the operation, or find the sequence of operations, answer. ” needed to solve the problem. 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Code P E Type of Error Prompt Explanation Identified an appropriate “Show me how you operation, or sequence of get your answer, operations, but did not and “talk aloud” as Process know the procedures you do it, so that I necessary to carry out can understand how these operations you are thinking. ” accurately. Correctly worked out the “Tell me, what is the solution to a problem, but answer to the Encoding could not express this question? Point to solution in an acceptable your answer. ” written form. 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City
Type of Code Error Prompt NE No Error 13 th National Convention on Statistics October 3 -4, 2016, EDSA Shangri-La Hotel, Mandaluyong City Explanation The student successfully completes the solution and gets the correct answer.
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