STEM Workshops 2014 Welcome!! Sandra Scott Jeanne Villeneuve Virginia Horowitz 1
Agenda Project Goals and Desired Outcomes Critical Thinking & Standards of Mathematical Practice Since I started teaching…. Big Problem “A Storm is Coming” Journals Culminating Task Big Problem “Museum Exhibit” Journals Smaller Problem “Planet Ork” Wrap up 2
Workshops and Project Goal Prepare students for STEM education and careers through applied academics 3
Desired Outcomes Standards of Effective Mathematical Teacher Practice Behaviors Critical Thinking Skills Student Student Engagement Behaviors Strategies 4
Desired Outcomes Participants will: Increase their familiarity with the Standards of Mathematical Practice Strengthen their inclusion of Critical Thinking Skills in their teaching Reflect on & incorporate reach-based effective teacher practices Increase the use of appropriate student engagement strategies in their teaching 5
Critical Thinking from Scheffer and Rubenfeld, 2001 1. Analyzing (Separating a whole into its parts) 2. Synthesizing (Bringing parts together to form a whole) 3. Applying Standards or Judgment 4. Discriminating (Similarities and Differences) 5. Information Seeking (Searching for evidence, facts and gathering data) 6. Logical Reasoning (Drawing Inferences or Conclusions) 7. Predicting (Envisioning a plan and its consequences) 8. Transforming Knowledge (Changing or converting concepts 6 from one context to another)
Some Student Engagement Strategies Small Group Discussions Thumbs Up/Down/Sideways Traveling Salesman Journals/Reflection Papers Quick Writes Hands-on Real World Applications Whip-around Exit Slips 7
Teacher Behaviors Organization & Planning Begin with the end in mind. What do you want your students to understand, to know and to be able to do? Use Open-ended questioning strategies. Be prepared with a set of good questions that further your students’ Critical Thinking Skills. Anticipate misconceptions and stumbling blocks. Use highly effective teaching strategies (e.g. Marzano’s 9) Model Thinking Aloud Make your expectations clear—at the beginning Think about your core beliefs about teaching and learning and 8 do your best to “live them”
Grouping of Practices 9
Since I Started Teaching… Life has been like… choose a book, movie, TV show, etc. because…………….
Since I Started Teaching Life has been like “A Thousand Splendid Suns” because ………… You can’t wait to see what each new day holds.
Since I Started Teaching Life has been like Seinfeld because…………… Weird personalities have dominated my days
Since I Started Teaching Life is like “Yellow Submarine” because……. My department is really coming together .
Since I Started Teaching Life is like a Monster commercial because ..... https://www.youtube.com/watch?v=npQC7v73TXg
A Storm is Coming An auger falls off a combine during harvest because the ball bearing failed. The steel balls fell off the machine onto the field over several yards making it impossible to recover and count the original number of balls needed to repair the auger. The parts store is several hours drive away, the harvest needs to be completed ASAP as a storm is predicted to hit in about 10 hours, you don’t have any measuring tools, and no time to return home to get measuring tools. You need to improvise. How can the number of steel balls be estimated to get an accurate count, go to the parts store, return, and repair the equipment before the storm? Bearing: A part of a machine that bears friction Ball Bearing: A bearing consisting of a number of hard balls running in grooves (called a race) in between two concentric rings. Ball Bearing Uses: Car wheels, skateboard wheels, roller blades, manufacturing equipment, farm implements, etc. 15
Collect and graph the data Due to the high cost of the bearing balls, you want to order only what you’re sure you need. In your truck you have some tubing and duct tape, as well as miscellaneous items in the glove compartment (your teacher will hand you a bag of these items). Additionally you are able to gather about 35 bearing balls from the ground. Decide with your group what unit of measure you will use to measure the ball bearing provided. You may use any of the items listed above, or anything on your person. With your group, determine how many “marbles” it takes to line each of the round items you have or can create. Record your data, then graph it. Use the graph to make a reasonable prediction for how many ball bearings you will need to purchase. Inspiration for this problem: http://searchingformath.com/2012/06/01/how-many-ball- bearings/ and Sandra Scott 16
Journals How might this problem be used in your classroom? What question(s) could you ask to increase students’ critical thinking during this exercise? 17
Using Graphing Calculators to determine linear regression. Follow the handout in the binder to enter your data and find the line of best fit. 18
Where, How and Why Could You Increase Your Use of Big Problems? Please Journal Your Response ... 19
Culminating Task – Workshop #3 Look for a familiar problem or one you would like to try with students—applicable to your grade level/course Teach this piece of a lesson to the group so that you apply what you have learned in the two workshops and reflect on your work Identify the CT Skill(s) and SMP(s) and the Student Engagement strategies you use Can work alone or with a partner—10 to 15 minutes per demo Questions? 20
M 3 The M useum of M odern M athematics plans to feature a new exhibit in the hall of Pi. They plan to hang an 8 foot diameter circle, filled with glistening round stones. The stones are each ¾ in diameter. How many stones will be needed to cover as much of the circle as possible without any overlap or any excess hanging outside the circle? 21
Find a Pattern Your group has several circles. Measure the diameter of each circle in inches (input), then cover the circle with as many pennies as possible (output). Record your data on the chart at the front of the room. Graph your data, and use it to predict how many stones would be needed for the museum ’ s exhibit. Can you create an equation that models your data? Try it here ________________________________________ 22
Alternatives and Variations Change the size of the circle to make the problem more manageable Use a graphing calculator to determine the equations of the: line of best fit, parabola of best fit, exponential of best fit. Online Version: https://class.desmos.com/pennies Inspiration: Dan Meyer, and Desmos 23
The Lab Rats 24
Journaling Write down the critical thinking skill(s) and SMP(s) you would focus on when you use this Big Problem. 25
Planet Ork Welcome to the workshop! Please read the problem below, and determine which clique each inhabitant was from. Be prepared to justify your answer. Mork took Mindy to the Planet Ork. One day, while sightseeing, they happened upon an odd looking township. Mork explained to Mindy that the inhabitants of this township all belonged to one of two cliques: The truth tellers (who always tell the truth) and the liars (who always lie). Just then, three of the inhabitants walked up to Mork and Mindy. “ We ’ re all liars ” said the first. “ Just one of us is a truth teller ” claimed the second of the three. The third did not speak. 26
WHY The Warm-up Problem? Warm-ups are an easy way to begin making changes in your curriculum. Problem solving often allows different types of students to “shine” This problem requires reasoning and construction of viable arguments Students can test and debate their solutions in small groups ≠ Mathematics Arithmetic 27
Whip Around and Evaluation You have the following handouts: 1. Student Engagement Strategies 2. SMPs 3. Critical Thinking Skills 4. Effective Teacher Behaviors Pick one item from one of the lists that you will pay attention to between now and our next workshop. Be prepared to announce it during our “Whip Around”. 28
Next Workshop: Friday, April 4 th 29
What Grouping of Practices Are You Most Comfortable With? 30
What Grouping of Practices Are You Least Comfortable With? 31
Who’s Your Favorite Bidder? Barry 32
How Many Years of Teaching Experience Do YOU Have? 33
Standards of Mathematical Practice 34
Wake UP!!! – Part 1 It is your job to order new cups for Wake Up , the coffee shop you work for. The computer is down, and the boxes that the cups come in have all been recycled, but you did notice the box was about the same height as your manager, Mrs. V. The operator at the Cups Are Us warehouse can take your order, but they don ’ t know how many cups come in a box. Discuss what information and tools you will need to figure out how many cups come in a box. 35
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