MIAA 320 Demonstration of Advanced Practice

1. MIAA 320 Demonstration of Advanced Practice Carla Bacchetti

2. What gets students excited and motivated to learn mathematics? • Classroom discourse is one way to get students excited about mathematics in the classroom; it is also an important strategy for getting your students involved in their learning. • Good questions are open ended, thought provoking, higher order thinking, contain transferable ideas (across subjects), create more questions, require a student to support and justify their answers, and over time reoccur. • Many classrooms focus on Lower-Level Demands questions that ask a student to reproduce facts and rules that are memorized, but as teachers we need to move to Higher-Level Demands, such as problems that require multiple representations and may involve some level of stress on the student to produce a thought provoking answer.

3. Sixth Grade Math Lesson Observation and Small Group Work • Lesson: Addition of fractions and finding the least common denominator • This classroom lesson was instructed by a well respected and effective teacher, but it was a very direct instructional lesson. • Many questions heard: (many lower-level questions) • Using the what? • Add or subtract the ______. • If you get lost where should you look? • How do we set up our fractions?

4. How do we set up our fractions? • Answer: Top to bottom. This surprised me because as I walked around I saw students who set up their problems horizontally. • I walked around to try out some questions on struggling students. I came across a student who needed to change 1 to a fraction in order to add. He needed a denominator of 18. • I asked, “How do you make a fraction out of 1? • Answer, “You put a 1 under it.” • Me, “Good, so what other fractions equal 1? • Answer, “2 over 2.” We worked on the board to make equivalent fractions 3 over 3……..18 over 18. • On a later problem that was similar I walked over to see if the student needed help and he didn’t. He understood it on the first try.

5. Algebra One Small Group Work • Lesson: How do you solve equations with variables on both sides? (Essential question) • After Cornell Notes, I worked with a group of four students and asked them questions as they worked through their problems. • Questions: What is a variable? What is a constant? Is it possible for an equation to have no solution? How do you know? Why is it important to get all of the variables on one side of the equation and constants on the other?

6. Group of Four • The group was not talkative with each other but did talk to me and ask questions. • Most of my questions were lower-level, such as why did you add 6 to both sides? • As the students worked on an equation with no solution, I asked, “Why is it important to move the values to opposite sides?” The student said, “You get the wrong answer (if you don’t).” He then realized that 4x – 4x is zero and that without a variable the solution is zero. • Finally I came across a student who solved his equations by just moving values to the opposite sides of the equation making sure to switch the sign as he moved them. I asked him to explain what he was doing. “When I move values to the other side it changes the sign whether it was a constant or a variable.”

7. Second Grade Lesson Using the Five Practices • Lesson: Writing Addition Number Sentences • Essential Question: What is a number sentence? (What would it look like?) • After grouping the students in to groups of 3 or 4. I would give them poster paper to illustrate the essential question. • Moving around I would monitor the discourse and be able to select which students I wanted to present first to guide the lesson for the other students (sequence). Knowing that some would represent with numbers and others with objects.

8. The Five Practices • Selecting first a student to show their representation of a drawing (5 apples on one side a 4 on the other) then selecting another student to share (using numbers), and finally (numbers, addition sign, and hopefully an equal sign). • Connecting: After the sharing of ideas we could then connect the picture representations with the actual number sentence. • Question: What must an addition sentence have or include? • Possible student question: Does it matter what number comes first?” • This question could start a discussion on the commutative property and further inquiry.

9. Conclusion • I think that students are very used to being taught mathematics using direct instruction strategies, and they do fine being given the information and steps needed to be successful. • But..when given the chance to think and discuss the process and how they arrived at an answer, the students seem to take ownership of their work and it becomes theirs. • I believe this creates a natural motivation for the student to become curious about their learning.