Read through the entire Chapter 4
Reflect on the following questions and comment below:
1. Have you ever been guilty of the Tricks in this chapter? If so which ones? Will you change the way you teach it in the future and if so, how?
2. Give an example of an effective way to teach vocab in the Geometry Unit of Math that you currently teach.
3. Comment on a colleagues post to engage in a meaningful conversation.
Im not a math teacher but as a science teacher I need to use math. I also try to help students with their math problems so I thought this course would help me be a better teacher. I have to admit when taking geometry I didnt completely comprehend. I thought the definition of a square was 4 equal sides ? I also thought Pythagorean theorem was an equation. I think an effective way to teach vocab would be to have students draw examples/pictures where possible not just the definition.
ReplyDeleteI agree Peter and APPLY what they are learning, im sure something you do very often in the Science world.
DeletePictures are a great way to foster discussion. This will help students understand the concepts. Again, if we had more time, we could give students the opportunity to make these discoveries themselves. As I stated in my post, most students will identify a square as a figure with 4 equal sides and a rectangle as a figure with 2 long sides and 2 short sides.
DeleteI have fallen to the a^2 + b^b = c^2 routine. But I also understand what was being said in the book where the students can't pull away from the a, b, and c. They get turned off when you say that when you have a right triangle you can just sum the squares of the legs and it will be equal to the square of the hypotenuse.
ReplyDeleteI will make sure I focus more on the sides of the triangles as legs and hypot. instead of letters. I will also start off by doing a problem that shows the pyth. thm. using another type of triangle to show the students that the Pyth. thm. is special to just right triangles. This will help teach roof pitch in Building Trades.
I can't say I am specifically in a particular Geometry unit because I teach at a trade school but we are working with shapes ALL of the time and their functions. I recently revamped a lesson for Taper in Machine shop. Taper is nothing but the slope formula and I taught the students the Taper formula which is (Large Diameter - small diameter)/Length. We talk about the change in vertical distance divided by the change in horizontal distance and then they see the relationship directly with the change in x over the change in y which is slope. If I were to just tell them to subtract a couple of numbers on their blue print and then divide they would have never absorbed that connection, that vocab and that content.
As a fifth grade math teacher, there are a lot of concepts I don't understand that you are talking about, but it helps me realize that tricks happen at any level or application of math. I like how you identified that if you were to just teach them the shortcut, they would never absorb the connection, vocabulary or content. Sometimes it is so important to skip the tricks.
DeleteSarah I'm looking forward to your lesson now on roof pitch in my class! That is such a challenging concept for my students as you know but this seems like another technique worth trying.
DeleteSarah
DeleteI would like to put together some nice posters for recipe conversion factors and the bakers percent. I think it will go well the the gallon posters.
I can honestly say that I have not been guilty of the tricks in this chapter. Sixth graders have a difficult time with 4.2 and 4.3, for sure. Preschoolers learn to identify a rectangle as a figure with 2 long sides and 2 short sides and a square as a figure with 4 equal sides. If I ask students to draw a rectangle, the majority of them will draw a figure with 2 long sides and 2 short sides. They will always have 4 right angles, but that isn’t what they focus on. I always enjoy teaching students how to classify quadrilaterals because it creates a lot of good discussion.
ReplyDeleteI think that the most effective way to teach geometry vocabulary is to simply get a discussion going in class. It is important to always use the terms angle and congruence. I feel that repetition will help students understand the concepts.
I have been guilty of 4.3, Squares have four equal sides. Squares do have four equal sides but you also have to add that they also have that they have four equal angles (90 degrees). Next time I teach squares, I will make sure I use what they wrote: “A rectangle with four equal sides”. I have also have been guilty of 4.4 Obtuse angles are Big. They shouldn’t see angles as “small or big” angles. Instead, they should be identified by their degrees and called the proper names. Obtuse angles are any angle over 90 degrees, and an acute angle is less than 90 degrees. I love using vocabulary in math. Geometry is loaded with rich vocabulary that students need to know to understand the concepts in geometry. I have the students keep a math vocabulary notebook in their binders and not only do they have to define the math vocabulary I assign, but the also have to draw a picture representing the math vocabulary word. I often make a poster of key geometry vocabulary and hang it in the room for the students to reference.
ReplyDeleteAudrey~ I love the idea of making a notebook for math vocabulary. I also think hanging posters is a great idea. I think if used properly they can peak childrens' curiosity. I remember when I worked in your classroom, we wrote the word PEMDAS all over the classroom and the hallway a week prior to that lesson. It drove the kids crazy and they couldn't wait to find out what it meant. That might be a bad example, because PEMDAS is a trick, but they did remember it when we taught the lesson!
DeleteHi Audrey! I think you probably see some of the same things I do. The modules are based on a more conceptual approach, so using tricks is not our first step in teaching curriculum, it usually comes at the end.
DeleteThanks for sharing Audrey! That is great, a lot of teachers forget how important math vocab is... math literacy!!!
DeleteAudrey, I'm such a visual learner I like your idea of drawing the pictures to represent the math vocab that would really help my students too I bet..
DeleteAlthough it might be tough to draw a picture of imaginary numbers...
DeleteAudrey and Kelly,
DeleteI LOVE the idea of hanging math vocabulary around the room before its introduced. What an excellent anticipatory set! Its a simple, easy, engaging way to get kids to ask the question you want to answer.
I currently have posters hanging in class but love the idea of having a math notebook. I think that's what I'm gonna work on this summer for my students.
DeleteI have used a few of the tricks from this chapter. One that stands out to me is 4.4 Obtuse Angles are Big and on the flip side, Acute angles are small. I am not sure that my students think about the length of the rays being big, like the book talked about, however, I am always careful to attach mathematical meaning to this “trick”. We do focus on the fact that an obtuse angle is and angle with a measure between 90 and 180 and acute angles are between 0 and 90 degrees. If the “trick” was taught in isolation then I agree it is not sufficient, however, once again, I do believe attaching a memory aid (such as acute angles are “cute” and tiny) may help them to make the connection to the actual definition.
ReplyDeleteWhen teaching geometry vocabulary I believe it is important to always attach visuals. It is easy enough to create the shapes around the room and write the attributes of each shape inside the shape. I like to put things up on the walls prior to the lesson so that children have some time to look at them and think about them.
I agree that attaching a memory aid is an acceptable way to help students make connections. It seems as the years go by the range of students gets wider and we want to reach all of our students.
DeleteI guess I am guilty of using the formula for volume. However, the book states that “These are not tricks, but if they are taught without context they become as magical as any other trick in this book.” As I have stated earlier, the CCLS and modules have created lessons that move through the conceptual understanding of volume, before we even look at using the formula for volume.
ReplyDeleteAn effective way to teach geometry vocabulary would be to use visuals or models. We have mini 3 models available for students to see and touch, but I also use items in the room. For example, most Kleenex boxes are rectangular prisms.
I love the idea of using visuals for teaching new vocabulary. This is something I sometimes forget. Visuals are definitely more effective at helping students recall important information.
DeleteI am very guilty of 4.8's method of KFSA (Keywords, Formula, Substitute, Answer). I use this method loyally! I use this in Earth science as well for density, gradient, rate of change. This method is generally very effective, but students are not genuinely learning the concepts, especially regarding surface area. It is very obvious where the formulas come from if students can visualize the net of the object.
ReplyDeleteI glanced at Janelle's and Kelly's response and feel that visuals are a very good way to teach vocabulary. When students can see the object, the image will be able to reappear when the vocabulary word is presented at a later time, enabling the student to draw a picture and make sense of a problem.
I am so guilty of teaching that acute angles are little and obtuse are big. But again, that is after teaching that acute are less than 90 degrees, etc. When students reach me in middle school, this is a concept that most understand. The same with Pythagorean thm, I teach right triangles and tell them the formula last. Going forward, I think I need to spend more time on concepts to help students develop a deeper understanding. I also teach vocabulary with examples, pictures, and having them write in their own words.
ReplyDeleteAs someone who teaches applied geometry.. I'm guilty guilty guilty. Mainly in 4.5 saying pythagorean using abc and also 4.7 converting 2 similar triangles into square/rectangle to find the area of a triangle. However, I need to try and justify why I still might. When I teach students to square a floor or wall I have them pull a tape measure across both diagonals if they are equal it is square if not then we need to move the one side 1.2 the distance of the difference of the diagonals. For instance they don't need to calculate a hypotenuse of a floor measuring 12' x 30' they just need to move the one side of the rectangle until they are equal. (Pythagorean applied) Then when I teach students to estimate siding on a gable end or roofing on a hip roof I find most of the time the triangle to square/rectangle conversion is very effective for me to understand but now I see why it might not be for my students. SO one thing I do is draw with colored dry erase markers this relationship and then they see the relationship since most of the time these are right triangles.
ReplyDeleteI am guilty of reinforcing 4.7 with the area of a rectangle is length x width. I don't like that triangles then use base and height. In 5th grade and reinforced in 6th is that a triangle is half a rectangle hence the formula. I like the idea of extending the idea of parallelograms instead of just thinking about the right triangle/rectangle connection.
ReplyDeleteFor teaching the definition of surface area the common core standard wants 6th grade teachers to have the students explore SA as drawing a net, find the area of the sides and adding them all together. I teach this after composing and decomposing irregular figures so its a natural extension. After many times finding the SA of rectangular solids many of the kids generalize the pattern to be similar to the formula. I love that!
I am guilty of reinforcing 4.7 with the area of a rectangle is length x width. I don't like that triangles then use base and height. In 5th grade and reinforced in 6th is that a triangle is half a rectangle hence the formula. I like the idea of extending the idea of parallelograms instead of just thinking about the right triangle/rectangle connection.
ReplyDeleteFor teaching the definition of surface area the common core standard wants 6th grade teachers to have the students explore SA as drawing a net, find the area of the sides and adding them all together. I teach this after composing and decomposing irregular figures so its a natural extension. After many times finding the SA of rectangular solids many of the kids generalize the pattern to be similar to the formula. I love that!
I don't exactly teach geometry in my class. I do feel that students need to know math terminology to fully understand math. Correct math vocabulary strongly correlates to comprehension and students expand their ability to reason.
ReplyDelete