Module Thirteen

Measurement Misconceptions

Why do you think the students are having difficultly?
I think the students are having difficulty because measurement with rulers might be something they have never done before. When we do something new for the first time without any instruction we most of the time do it wrong. 
What misunderstanding are they demonstrating?
The misunderstanding they are demonstrating is how to correctly use a ruler. Some students don't know how to use a ruler and don't know you have to start at the 0 mark. Some don't understand what the marks on a ruler mean. And some students just want to guess.
Have you witnessed any students experiencing some of these same difficulties?
I haven't had the change of working with students on measurement in my field experience so no I have not witnessed this.
What types of activities could you implement that would help these children?
 I would try to find online resources like videos or games that would help the students better understand how to use a ruler.

Why do you think so many students have such a hard time with measurement?

TCM Article- Rulers

The ideas that I took away from this article that it is important to teach students about spatial measurement. They sometimes need to know how to measure things when they don't have the numbers on them. It shows the students that they really need to pay attention to the lines on a ruler and what they might mean. The possible misconceptions that children might have about measurement is that items measurement can be different depending on how the item is measured. 

Angles Video and Case Studies

Many of the students described angles as spaces between two lines when they connect. One student thought that an angle could have curved lines. That is the only explanation of an angle that I thought didn't make sense. I think many of the students had a hard time explaining what they meant though when trying to show what they meant with their hands and arms. 

If you were to describe an angle would you describe is any differently than the students in the video did?

1. In Nadia’s case 14 (lines 151-158), Martha talks about a triangle as having two angles. What might she be thinking? Martha is seeing the triangle as BAC and BCA when she need to also see it as ABC in order to see all the di fferent angles of the triangle. 
2. Also in Nadia’s case (lines 159-161), Alana talks about slanted lines as being “at an angle.” What is the connection between Alana’s comments and the mathematical idea of angle? I think Alana means that the lines are perpendicular to one another but just couldn't think of the word. This means that at some point the lines with intersect with one another to form a angle.  
3. In Lucy’s case 15 (line251), Ron suggests that a certain angle “can be both less than 90˚ and more than 90˚.” Explain what he is thinking. Ron thinking is right in this case because it depends on how you look at the angle. He knows that a straight line makes up a 180 degree so that one part of it would be less and another be more. Depending on how you look at it it changes the degree of the angle. 
4. In case 13, Dolores has included the journal writing of Chad, Cindy, Nancy, Crissy, and Chelsea. Consider the children one at a time, explaining what you see in their writing about angles. Determine both what each child understands about angle and what ideas you would want that child to consider next. Chad- Needs to understand that the degree of an angle does not depend on how long the line is. Cindy- Understands the concepts of what an angle is but need to work on the terms of the different parts of an angle. Nancy- I would make sure she understood that big means more than 90 degrees and light is less than. And that there is also an angle that is called a right angle that equals 90 degrees. Crissy- Knows what a right and obtuse angle are. Needs to understand what an acute angle is. And also understood that all angles are sharp. Chelsea- Needs to write what they definition of an acute angle is. Needs to include obtuse and also need to describe what the boxes in the shapes are. 
5. In Sandra’s case16 (line 318), Casey says of the pattern blocks, “They all look the same to me.” What is he thinking? What is it that Casey figures out as the case continues? Casey is thinking that the angle is just the point not the area of space between the two lines. As the case continues he realizes what an angle is and how to figure out the degree of an angle. 

How Wedge you Teach?

It surprised me that fifth grade students still struggled with measurement and angles since this is something they have been dealing with for many years now. It makes me really think that this is a concept that will need to have a lot of attention on and needs to have many hands on activities for the students so that they can better understand it. 

Exploring Angles with Pattern Blocks

• Green Triangle: 3 Congruent Angles at 60 degrees 
• Blue Rhombus: 2 acute angles of 60° and 2 obtuse angles of 120°.
• Red Trapezoid: had 2 obtuse angles of 120° and 2 acute angles of 60°
• Tan Rhombus: 2 acute angles that were 30° and 2 obtuse angles that were 120°.
• Yellow Hexagon: 6 congruent angles at 120 degrees.

Did you have any difficultly with any of these? If so, Why?

For Further Discussion

I feel like everyone uses nonstandard measurements daily. I use to work at a bagel and coffee shop and people would always ask for "a little bit of cream" for there coffee or "a tiny bit of cream cheese" on their bagel. I now work as a nanny and if the kids ask something I sometimes say "in a little bit" because I am in the middle of doing something at that moment. Also whenever I go to dunkin I order an unsweet tea with 2 splenda sometimes they dont have the splenda packs but know how much to use because of what I said. 

I think nonstandard measurement is sometimes just easier to use because we don't always have regular measurement devices on hand. 

Do you use nonstandard measurement often?