MATH:
JEAN MARIE STEIN
INQUIRY RESULTS, 2013..............................................................................................
Sleepy Hollow High School
New York, NY |
Jean Marie Stein is a Mathematics Teacher at Sleepy Hollow High School in Sleepy Hollow, NY (near Tarrytown, NY).
Sleepy Hollow High School serves an ethnically and socio-economically diverse student body from the villages of Sleepy Hollow and Tarrytown. Recently renovated and expanded, the school stands above the east bank of the Hudson River in southern Westchester County, approximately 20 miles north of New York City.. jstein at tufsd.org |
Inquiry Title:
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Learning Probability through the Use of Inquiry Based Lessons
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Inquiry Questions:
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If I specifically model problem solving skills over a period of four months leading up to the probability inquiry unit, will students be able to discover and internalize the basic concepts of probability? Will their engagement in the learning process and their ownership of their learning process increase?
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Contextual Information..................................................................................................
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What I did:
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For months leading up to the Probability Unit, I tried to foster problem solving techniques in daily lessons and homework review in hopes that they would be able to work independently on the probability unit.
Just before the unit began, after the previous unit’s test, I gave a survey that asked what the students knew about probability. Most wrote that it was the chance that something would happen. One reported that it was always stated in percents. I began the unit with a horse race game on the Smartboard. There were 12 horses at the start gate (numbered 1-12) and a pair of dice. Each roll of the dice would determine which horse moved. A horse would need to move seven times to win. I explained how the horses would be moved and showed them how the dice would roll. Each child then chose a horse with the understanding that there was no limit to how many children could choose the same horse. In both classes, their lack of understanding of probability was evidenced by their choices: Nearly every horse was chosen, including Horse 1 (the impossible event). ( See Image 1 below) The students were very engaged during the “race”, but accused me of fixing the dice because too many 6s, 7s, and 8s were coming up. I took out real dice and let them do the rolling to eliminate their suspicions. After the race, we discussed what happened. They concluded:
The next day, they conducted an experiment in which they worked in pairs to roll one dice 50 times. They answered a series of questions that led them through the idea of theoretical probability and had them compare theoretical probability to their experimental data. (See Image 2 below) The students then entered their individual data into a prepared excel file. They observed the class data as a whole. Discussion ensued. Empirical Probability when looking at the class totals. (See Image 3 below) The students then entered their individual data into a prepared excel file. They observed the class data as a whole. Discussion ensued. Empirical Probability when looking at the class totals. (See images 4 & 5 below) |
Special Resources utilized in this inquiry
(i.e. websites, apps, books, etc.): |
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Data Evidence Plan
Data Sources |
Central Content Ideas Measured |
Measurement Tools |
Data Source 1
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Previous knowledge of Probability: Level of interest in the topic.
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Two question survey after a test: What do you remember about probability?
What would you like to know about probability? |
Data Source 2
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Engagement in Unit: Assessed interest in the topic, enjoyment of the unit and whether they found themselves thinking about probability.
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Questionnaire
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Data Source 3
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Understanding of Probability
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Unit Exam
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Data Source 4
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Engagement in Unit
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Homework completion
Classroom behavior |
Summary of Results..........................................................................................................
Results of student inquiry in
terms of my learning goals: |
Students showed growth in their engagement in mathematics as evidenced by their strong response concerning how often they thought about probability. A few students also displayed active interest in the lessons, one even came in during lunch to complete his dice rolling as he had been absent. He was pleased to see that the addition of his data made a difference in the class data – moving our experimental probability for each possible outcome closer to the theoretical probability of each outcome.
Students showed a better understanding of a topic learned through inquiry methods than a topic in which they were merely “told” what to do. This was evidenced by the results of their unit assessment. |
Evidence that was most useful to me in this
inquiry and what it reveals to me: |
The results of the unit assessment were most eye-opening to me. I saw first-hand the difficult y my students have remembering material if they have no relationship to the topic. When I gave them a rule for how to write set builder notation, it had no meaning to them. Those students who are good at memorization, were able to master the set notation work, but the majority of my students failed to achieve mastery.
I realize that I need to make every topic tangible. If I can’t, I need to come up with ways to get them to engage with the material in a more meaningful way – perhaps through group work or presentations. If I want them to grasp the language of mathematics, I need to linger a little longer on definitional type topics. I also saw clearly how well they understood probability and how a simple game could get them cheering and involved to the extent that they thought I had rigged the game! They all wanted to understand that the dice were not “fixed” - we were just experiencing the results of probability. It was nice to see my students come alive. This motivated me to try to provide more inquiry based lessons. |
What my results suggest about
my initial inquiry question(s): |
My inquiry question was very broad. I did not accurately measure the student’s ownership of their learning process at the onset, thus it is difficult for me to accurately assess growth in this crucial area. Also, although I modeled problem solving for them, I did not foster enough experiential learning.
On the other hand, they showed good growth in their conceptual understanding of the unit as a result of engaging in the inquiry process. |
Attitudinal Questionnaire:
Students were asked 6 questions concerning the unit and were able to answer strongly disagree, disagree, agree, strongly agree. At first look, nothing stood out. I realized that asking students if they “enjoyed” the homework was probably a poor question and asking if they completed more homework was also difficult for them to answer as 75% generally complete all their homework and the other 25% don’t do homework. (See Questionnaire Image 1) I grouped the responses more tightly into categories of favorable or not favorable. This highlighted a large difference on two questions: 18 out of 26 students said they understood the unit better and19 out of 26 students said they found themselves thinking about probability. (See Questionnaire Image 2) |
Unit Assessment:
A unit test was given. Initially, results were disappointing, with test scores similar to previous test scores on other units. However, analysis of each question separately showed that there were significantly more wrong answers on the two topics that had not been taught through inquiry. In fact, less than 30% of the students answered these questions correctly, compared to well over 80% of the students answering the probability questions correctly. A bar chart showing the topic of each question and the percentage of correct answers is shown below. (See below image) |
Samples of Student Work...................................................................................................
Examples of Student Work
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Quotes From Students
About What They Learned “…I
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Reflections: Backwards Look and Forwards Look........................................................
What I have learned about Inquiry:
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I have learned that inquiry helps my student’s conceptual understanding of a topic and that if I can’t provide an inquiry-based lesson on a topic, I need to allow them to find ways to make meaning of the topic.
Additionally, the inquiry lesson itself was actually very difficult to implement. Many students were reluctant to engage in any independent work. Many continue to be very uncomfortable with not being “told” the answer. I reviewed the activity with the students before we began, but the majority of students were uncomfortable following directions at their own pace and wanted me to hover over them as they filled in their results. I realize they are very dependent and very worried about making errors – even when there could not be an error in rolling a die! I had to really push them to work on their own. Once they finally realized I was not going to count their rolls, nor fill in their charts, they started to allow themselves to do the job. I think in mathematics class they expect a right or a wrong answer and are insecure with the idea that they sometimes need to explore many answers. Next year, I will foster experiential learning throughout the entire year. I hope this will alleviate some of the insecurity my students feel with the process. |
What's next for my students and my teaching approach:
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I will be engaging in curriculum work this summer for implementing the Common Core in Integrated Algebra/Algebra 1. I plan to provide inquiry based lessons early in the school year so that inquiry will be integrated into the full year course. I will work to move my teaching to a more student- driven and less teacher- driven model. I recognize that next year will be challenging as I face the pressure of implementing a new curriculum, but that this curriculum lends itself to allowing students to go deeper into a topic to create a deeper understanding.
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How I plan to share my results with the community:
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