Читать книгу Mathematize It! [Grades 6-8] - Kimberly Morrow-Leong - Страница 10

Imagine you are a new teacher. You are teaching eighth grade at a new school and are eager to get to know your students—their interests, skills, and how prepared they are to meet the challenges of eighth grade. You have just emerged from your teacher education program knowing various approaches you have seen modeled in classrooms and described in the literature, some of which you have tried with varying degrees of success. You aren’t sure what approaches you want to use but are excited about challenging your students, introducing the rigor you have read so much about. But first, you need to know what your students can and can’t do.

You decide to start with a couple of word problems, ones that involve relatively simple mathematical operations:

Mrs. King wanted her American history students to do a project about the Emancipation Proclamation. of the class chose to make podcasts. The other 9 students chose to create graphic novels. How many students are in Mrs. King’s American history class?

Armando started his descent into the cave. He was 10 feet down before he realized that he had forgotten to bring a flashlight. He climbed back up to the 2-foot mark to take the flashlight his friend handed to him. How many feet did he have to climb to get the flashlight?

You circulate around the room, noting who draws pictures, who writes equations, and who uses the manipulatives you have put at the center of the table groups. While some students take their time, quite a few move quickly. Their hands go up, indicating they have solved the problems. As you check their work, one by one, you notice most of them got the first problem wrong, writing the equation . Some even include a sentence saying, “6 students will do a podcast.” Only one student in this group draws a picture. It looks like this:

Even though the second problem demands an understanding of integers, a potentially complicating feature, most of these same students arrive at the correct answer, despite the fact that they do not write a correct equation to go with it. They write the incorrect equation 10 − 2 = 8 and are generally able to find the correct answer of +8, representing an 8-foot climb toward the cave opening. Some write K C C above their equation. You notice that other students make a drawing to help them solve this problem. Their work looks something like this:

To learn more about how your students went wrong with the history assignment problem, you call them to your desk one by one and ask about their thinking. A pattern emerges quickly. All the students you talk to zeroed in on two key elements of the problem: (1) the portion of students who did a podcast () and (2) the word “of”. One student tells you, “Of always means to multiply. I learned that a long time ago.” Clearly, she wasn’t the only student who read the word of and assumed she had to multiply by the only other number given in the problem. While a key word strategy led students astray in the first problem, visualizing the problem situation in the second problem led students to a correct answer, even if they were not able to write an accurate equation for the problem situation.