1. Teach Equation Solving Kathy Hawes Discussion presented by Jessica Dow and Janice O’Donnell

2. Purpose: Educate teachers on techniques to help students find and correct their own mistakes, as well as encourage students to read, discuss and communicate mathematically. Focus: Provide teachers with activities to create error analysis discussions that focus on students thinking, reasoning and ability to communicate mathematically. Audience: Elementary, Middle or Secondary mathematics teachers. NCMT Standards – Communication Process Standard organize and consolidate mathematical thinking through communication communicate mathematical thinking coherently and clearly to peers & teachers analyze and evaluate mathematical thinking and strategies of others use language of mathematics to express mathematical ideas precisely

3. Teacher writes a problem on the board and calls a student up to write the first step on the board. The student explains what he/she is doing in each step. The student passes the pen to another student for the next step. If another student has a question, the student holding the pen must explain their reasoning or answer the question. If the students makes a mistake, they can call on another student for help. Alternate solutions to problems are written on board as well. The role of the teacher is to enforce and enhance discussion by asking questions that will take the discussion deeper. Activity 1 – Pass the Pen

4. Strengths Everyone has a turn with the pen and discussion involves all students. Students learn to speak mathematically since they are required to explain their reasoning. Students see alternate solutions and choose ones that make most sense to them. Student feel empowered as they are running the discussion. Students that have difficulty simultaneously taking notes and copying ideas will have. time to process each step and comprehend process better. Weaknesses Unless teacher does many examples, not everyone will have a turn at board. Takes a lot of time – one problem could take the whole class with discussion. May not be effective in all classes – teacher must notice students having difficulty with a concept.

5. The students create a binder with all the correct solutions to problems they missed on homework or a test by consulting a different “Expert” for each missed problem. An Expert is someone who solved the problem correctly. The Expert does not show his/her work to the other student (Questioner), but helps find the mistakes of the Questioner and answers his/her questions. The Questioner is to ask enough questions to be able to write the correct solution on the binder paper. The teacher can provide lists of experts for each question or allow students to find them on their own. The role of the teacher is to model good questioning and monitor the process and discussion. Activity 2 – Find an Expert

6. Strengths The rules of this activity encourage students thinking as the Questioner must ask questions and the Expert explain their mathematical solution in words. Students are encouraged to do their homework so they are able to participate. Students enjoy the opportunity to move around the room and work with different students. They also appreciate playing different roles. Weaknesses If a student does not do their homework, they are left out of the activity. Students might notice that one student excels and flock to that student for expertise. Students communication skills might be weak, so understanding after explanation might not be complete. Might take a lot of class time.

7. Students provided with a problem that has errors. Students collaborate with each other to find errors and explain them, then describe them in journal entries. Teacher evaluates journal entries to assess understanding. Activity 3 – Journal Writing

8. Strengths Careful reading of student’s responses will offer insight into their level of understanding. Gives the teacher an opportunity to provide feedback to individual students. Since journals are seen as a personal activity, students are less likely to share or copy from someone else. Improves students writing and explanation skills. Weaknesses Students might not understand why they are writing about mathematics if not explained well.

9. Teacher creates an error analysis take home project/exam or in-class exam with at least 2-3 errors in each single example. Activity 4 – Exams and Take Home Projects Strengths If teacher allows, students can collaborate and help each other on take home projects. Take home projects allow students more time to think about problems and demonstrate their knowledge. Students have opportunity to express mathematical thinking more thoughtfully. Weaknesses Students might be tempted to copy answers.

10. Strengths of the Article Touched on a variety of learning styles: Logical (mathematics), Spatial (visually seeing errors as they occur), Kinesthetic (moving around in groups or getting up in front of the classroom may interest student), Verbal (speaking in mathematical language, asking/answering questions and journal writing), Interpersonal (group work or playing different roles), Intrapersonal (reflecting and writing in journals). Student-centered activities that increase teacher insight into student’s misconceptions. Students examples are provided for ¾ activities. Quotes from NCTM standards. Can be used in other academic areas.

11. Weaknesses of the Article No mention of how to use technology. Methods used for solving equations only – no examples for other mathematics topics.

12. References Teach Equation Solving, Hawes, Mathematics Teaching in the Middle School, v12, p23-242 www.npr.org/templates/story/story.php?storyId=1914784 NRP article about importance of insight into student’s math errors