Building a Community of Learners

1. Fall 2008 Building a Community of Learners

2. Profile of Developmental Student • Activity • Individually, list the characteristics of the students in your developmental math classes on a sheet provided. • Then, with your group, list the common characteristics of these students. • Be prepared to share your list with the large group.

3. What Do We Know About Characteristics of Students with Math Problems? • Fail to verify answers and settles for first answer • Cannot recall number facts automatically • Take a long time to complete calculations • Make "borrowing" (i.e., regrouping, renaming) errors • Count on fingers • Reach "unreasonable" answers • Calculate poorly when the order of digit presentation is altered (Bryant, 2000)

4. What Do We Know About Characteristics of Students with Math Problems? (cont.) • Order and space numbers inaccurately in multiplication and division • Misalign vertical numbers in columns • Disregard decimals • Fail to carry (i.e., regroup) numbers when appropriate • Fail to read accurately the correct value of multi-digit numbers due to order and spacing • Misplace digits in multi-digit numbers • Misalign horizontal numbers in large numbers • Skip rows or columns when calculating (Bryant, 2000)

5. How Do You Create a Safe Classroom Environment?

6. Instructor Role in Creating a Safe Class Environment • Create a warm, caring, supportive environment • Learn and use student names • Encourage questions • Model respectful behavior • Involve students in decision making • Provide opportunities for student leadership • Develop effective problem solving strategies (Brownlie & King, 2000)

7. Student Role in Participating in a Safe Classroom Environment • Share ideas • Respect other students and instructor • Feel free to ask questions and take risks • Support and encourage each other • Work together cooperatively • Assume responsibility for learning and behavior • Make decisions for own learning • Learn other students’ names (Brownlie & King, 2000)

8. Activity • In your small groups, post-it notes to list three benefits (green) and three challenges (yellow) of students working together in groups. • When your group has completed the 6 post-it notes, please select a representative to place the notes on either the benefits chart or the challenges chart.

9. Traditional Classroom vs. Community-of-Learners Classroom (Wang, 2007)

10. Activity • Four volunteers needed • While the volunteers are preparing, consider the following questions during the role-play: • What is the instructor doing well? • What might the instructor do differently? • What are other potential solutions to the scenario? • Please do not share any student-specific stories .

11. Think/SpeakAloud Thinking Aloudinvolves one person saying out loud the steps and mental work done to perform an academic task (Artzt & Armour-Thomas, 1992) If subject matter expert is thinker-speaker • allows modeling of thinking • shows students how to approach/think about material • permits students to hear what goes on in an expert's head • externalizes of expert’s feelings • helps students learn to self-regulate

12. Think/SpeakAloud Thinking Aloud involves one person saying out loud the steps and mental work done to perform an academic task (Artzt & Armour-Thomas, 1992) If student is the thinker-speaker • provides student with valuable process even when student is alone • allows student to be more aware of what goes on in his/her head • provides real insight into improving performance • assists students to be more systematic in thought processes • helps students catch errors early

13. What the Speaker Does • Translate thoughts, ideas, images into words and speak aloud • Verbalize all steps used to solve problem. • No thought too small, easy, obvious, or unimportant • Verbalize thinking before beginning to solve the problem • Even second-guessing is important • Verbalize thoughts during problem-solving (Artzt & Armour-Thomas, 1992)

14. What the Listener Does • Allow the speaker to express themselves without interruption • Pay attention to the speaker voicing opinion and preferences • Listen for voice fluctuations • Watch for facial and other non-verbal cues • Ask questions after the speaker has finished

15. Think/Speak Aloud Problem The US government has been in the bailout business lately. For example, AIG received $85,000,000,000 in September to avoid bankruptcy. The current US population is about 306,000,000. On average, how much does this bailout cost each US citizen?

16. Think/Speak Aloud Modeling The Model: • I have two quantities; what am I supposed to do with them? • The problem asks to determine how much the bailout costs each person. This implies that I need to do division. • The numbers are rather large; is there a way to express them in a condensed form? I can rewrite them in scientific notation. • I have the problem set up; I know exponent rules and how they apply to operations with scientific notation. • Does my answer make sense?

17. Think/Speak Aloud Listener Expectations • Take notes when the person is speaking • Explain the purpose of the listener’s feedback • Be positive and encouraging about the speaker’s thinking process • Point out strengths and weakness

18. Think/Speak Aloud Activity • Find a partner • Open your folder • Each partner should select a different Think/Speak Aloud scenario • Read the scenario and then practice Think/Speak Aloud model with your partner • Each person takes a turn speaking and listening

19. Additional Notes • Remind of the process for both speaker and listener • Speaker must be allowed to go through the entire process • Provide positive encouragement for everything that is said (no right or wrong) • As the instructor • If using in the classroom, you must model the process • Do not take over, let the student work through the entire process on his/her own

20. Solve the Problem • Individually, take about two minutes to solve the following problem. • According to National Public Radio, 137 million Americans voted in the 2008 Presidential election, which accounts for 64% of all registered American voters. What is the total number of registered American voters? Round your answer to the nearest whole number.

21. Alternative Solution Approaches • For the rest of the session, you are going to participate in some alternative methods for teaching mathematics • Dot Addition • Stepladder Subtraction • Lattice Multiplication • Alternative Division • Others?