E1,+Where+and+Why+is+it+Wrong?


 * __Name of PEEL Procedure: E1, Where and Why is it Wrong? __**

**1) Summary of Procedure: ** Students are given a math problem that has been completed incorrectly somewhere within the problem. They are then asked to do three things with the problem. 1. Circle the **FIRST** line where an error occurs 2. Provide the **CORRECT SOLUTION** to the problem 3. Clearly **EXPLAIN** what was corrected and **WHY**. (ie what mistake was made?) Some questions given during this exercise may not contain errors. (Peel Publications, 2009)

**2) Strengths and weaknesses of Procedure: ** (Peel Publications, 2009)
 * **Strengths ** || **Weaknesses ** ||
 * Students think critically about the steps in the problem || Students may get confused about steps in an algorithm if they are unfamiliar with the question type ||
 * Students evaluate their prior math skills by checking an answer || Students may interpret the question incorrectly and correct the first line to make the math correct in the question ||
 * Students evaluate their own common mistakes by seeing them on paper and correcting them with an explanation ||  ||

**<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">3) Explanation why this is beneficial to student learning: ** <span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">Students differentiate why a question is right or wrong and critically think about the steps taken within the question. This evaluation causes students to think about the math they do on tests and exams and how easily it is to make a mistake. This may also cause students to go back and check over their answers on a test or exam, hopefully resulting in fewer minor errors.

**<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">4) 3 examples of the procedure: ** <span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">a. MCR3U (Grade 11 Functions). Students determine whether algebraic expressions are equivalent. The teacher could make errors when evaluating one expression and find that they are not equivalent.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">b. MHF4U (Grade 12 Advanced Functions). Students use trigonometric identities to solve trigonometric equations. The teacher could use frequently seen mistakes by students to have students evaluate the functions.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">c. MAP4C (Grade 12 Foundations for College Mathematics). Students learn about personal finance and technology. The teacher could show a spreadsheet with calculations and have students find the mistakes within the spreadsheet. The teacher could also show a problem where the mortgage or interest has been calculated incorrectly.

**<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">5) Curricular expectation for each example: ** <span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">a. MCR3U, A3.4 determine if two given algebraic expressions are equivalent (i.e., by simplifying; by substituting values)

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">b. MHF4U, B 3.3 recognize that trigonometric identities are equations that are true for every value in the domain, prove trigonometric identities through the application of reasoning skills, using a variety of relationships, and verify identities using technology

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">c. MAP4C, B1.3 solve problems, using technology, that involve the amount, the present value, and the regular payment of an ordinary simple annuity (Ontario Ministry of Education, 2007)

**<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px;">6) How each example is related to student’s lives: ** <span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">a. In the future, students may need to figure out shared costs of renting an apartment. They may need to figure out utilities and rent and compare two different situatio <span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">ns. This exercise will remind them to double check their math when they are dealing with money in the future.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">b. Students may use these skills if they choose to pursue further math education. They may also need to use trig identities in future jobs.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">c. As students work toward living on their own, they will need to budget and most of them will find it beneficial to set up spreadsheets or use templates and rearrange them. This is a way that students can see how easily a spreadsheet can yield unfavourable results.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; line-height: 23px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 0px;">Written by Amy Kelland

=<span style="font-size: 1.4em; margin: 0px; padding-bottom: 0px; padding-left: 0px; padding-right: 0px; padding-top: 5px;">**<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 22px;">Works Cited ** =

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">Ontario Ministry of Education. (2007). The Ontario Curriculum Grades 11 and 12 Mathematics. Queen's Printer for Ontario.

<span style="color: #008080; font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 16px; margin: 0px; padding: 0px;">Peel Publications. (2009). PEEL in Practice. Retrieved December 2010, from PEEL Project for Enhancing Effective Learning: <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; cursor: pointer; padding-right: 10px;">[]