Response to Marian Small's Question #5 - Create a Math Lesson

Pg. 651 #5: Lesson plan and Notebook PDFs. I will show the actual interactive Notebook in class but Blogspot will only allow me to upload images, text, and video to my blog post, not Notebook files.

Lesson: Transformations Using Notebook	Grade 5 Geometry & Spatial Sense
Critical Learning	Guiding Questions
Students will identify, describe, create, and analyze the three types of transformations using technology including Notebook Software and MacBooks in this cumulative activity.	What is a reflection? What is important to know when describing a reflection? (ie. line of symmetry, etc) What is a mirror line? What is a rotation? What is important to know when describing a rotation? (ie. direction of turn, which fraction of a turn, etc) What is the difference between clockwise and counter-clockwise? What does a quarter, half, three-quarter turn look like? What is a translation? What is important to know when describing a translation? (ie. number of spaces up/down or left/right, etc) What does congruent mean?
Curriculum Expectations	Learning Goals
Students will create and analyze designs by translating and/or reflecting a shape, or shapes, using a variety of tools (e.g., geoboard, grid paper, computer program).	Learning Goals (Unpacked Expectations) At the end of this lesson, students will be able to: identify and describe a reflection, rotation, and translation of a shape choose a regular polygon and create 3 questions (one for each transformation) that will move their chosen polygon across the Notebook page create an answer page for each question

Instructional Components
Readiness Students should have prior knowledge of using a MacBook and Notebook software. Since this is a cumulative activity, students should have prior knowledge of transformations. Students should have prior knowledge of fractions - quarter, half, three-quarters Students should already know clockwise versus counter clockwise directions Terminology transformation, translation, reflection, rotation, symmetry, mirror line, congruent	Materials class set of MacBooks with Notebook software Smartboard to demonstrate lesson to the class Document Camera Math Makes Sense textbook if they so choose “Transformations” Notebook file

Lesson: Transformations Using Notebook	Grade 5 Geometry & Spatial Sense
Minds On Approximately 15-20 minutes	Pause and Ponder
Explicitly identify the lesson’s learning goals as listed above. Create a positive classroom climate: welcome students, invite them into the Smartboard lesson Go through “Transformations” Notebook review lesson on the teacher USB stick.                                                      Review each slide of math vocabulary, types of transformations, sample questions                    for each type of transformation, answers to transformation, success criteria                   checklist.               Give an example of what a Level 3 answer looks like versus a Level 1 and have                  class answer why each grade would be given (ie. what are they forgetting in the                   level 1 answer).	Assessment as Learning (AaL) Students will be assessed on the 6 slides they create (one for each transformation and one for each answer page). Students will be graded according to the success criteria checklist. Differentiation (DI) Students will identified special needs will be partnered with capable students and will complete the activity with their partner. Quick Tip Are all students participating in the activity? If not, see if they need assistance and redirect. Link and Layer Using the document camera, show last week’s pen and paper transformations the students did in their math workbooks and explain they’re now doing that only on a MacBook. Hyperlinks in the Lesson - None
Action! Approximately 30 minutes
Students will log on to their individual MacBooks using their class password. Create new Notebook file and title it appropriately. Begin assignment in accordance to Success Criteria checklist (leave this up on the Smartboard for them to follow and refer back to). (Special Needs Student list partners are on your desk. These students work with their assigned partner in this assignment. Make sure you regularly check up on them that they’re contributing to the assignment as well.)
Consolidation Approximately 5-10 minutes
Have students use a copy of the Success Criteria Checklist to give themselves a level in each area of the checklist. You will use this when you use the same checklist to assign them a grade yourself.

A Mathematician's Lament Response

Do you agree or disagree with the points made in the article? 

I agree with so many points in the article. It was a long read but it held my interest and even had me laughing out loud at points. 

Why or why not?  

The following are just some of the points that resonated with me in agreeing with the article.

"Mathematics is an art." - It might not be an art form with myself personally, but I agree with this statement in that it's an art form to some. 

"The only way to get at the truth about our imaginations is to use our imaginations, and that is hard work." - Math most certainly is hard work.

"That little narrative is an example of the mathematician's art: asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations." - I've never thought of math like this; however, I believe this to be true. 

"By removing the creative process and leaving only the results of that process, you virtually guarantee that no one will have any real engagement with the subject." - I completely agree with this statement. This is similar to what Piaget writes about. Math needs to be made real in order for it to mean something to the person. 

"By concentrating on what, and leaving out why, mathematics is reduced to an empty shell." - I also agree with this. Math these days is more about quantity, not quality. We have so much to cover that it all has to be touched on but there's no time to understand the why. 

"Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity, you deny them mathematics itself." - This is kind of what is being taught now with students using pictures, numbers, words, expressions, or verbal to discuss their math reasoning. 

There is a "lack of mathematics in our mathematics classes." - I've never thought of this idea before but after reading the article, it's a very true statement. 

"Beethoven could easily write an advertising jingle, but his motivation for learning music was to create something beautiful." - I love this analogy. It makes a lot of sense when applied to math. Math should be more than just filling out question sheets, but it should be about creative expression instead. 

"If everyone were exposed to mathematics in its natural state, I think we would see a dramatic change both in the attitude of students towards mathematics, and in our conception of what it means to  be "good at math." - I laughed at this too with math being described "in it's natural state." It sounds like animals in the wild. LOL. But at the same time, I realize that math has been too far stretched and misshaped from it's original form that it's no longer fun. It's no longer freedom. 

"They're not learning anything now! Better to not have math classes at all than to do what is currently being done." - This is a pretty sad statement for a mathematician to make but there's truth behind it. We can't keep continuing with teaching math the way it is now. It's not working. These methods we're forcing on our students are actually hurting them and hindering their thinking abilities and creative reasoning abilities. 

"There is surely no more reliable way to kill enthusiasm and interest in a subject than to make it a mandatory part of the school curriculum and standardized testing." - Don't even get me started on the horrible effects of standardized testing. It makes confident students into second-guessing, scared to get the answer wrong, students who don't want to take any risks with their mathematical reasoning. It doesn't encourage them to do better. It hurts the advanced students and it decimates the struggling students confidence and makes them feel even worse at the competition they're never going to win. 

You don't need to try so hard to force math to be interesting and relevant, it already is! - #truth

"Give your students a good problem, let them struggle and get frustrated. See what they come up with. Wait until they are dying for an idea, then give them some technique. But not too much." - We've even talked about this very concept in this math course. One teacher said she spent an entire class devoted to one single question and most of the students finally came up with the answer on their own and were so proud of themselves. She said it would be nice to be able to do this more often because the math that day was real. It was hard. And they solved it. But she mentioned she has to get through the rest of the HUGE math curriculum so there's no time to devote an entire class to one question because so much needs to be covered. 

"Mathematics is an art, and art should be taught by working artists." Teachers don't need to be mathematicians but "shouldn't they at least understand what mathematics is, be good at it, and enjoy doing it?" - Math on a rotary basis? Is this the way of the future? 

"It is simply too early for that kind of technical training. It ultimately does more harm than good. Much better to wait until their own natural curiosity about numbers kicks in." - This again, reminds me of Piaget and his theories about stages of development children go through when learning math. A lot of time, they just simply aren't ready to do the math that's presented to them. Not that they can't eventually or can't be taught. Just not right now. 

We should play games with children in math class to help them become active and critical thinkers. - I love this idea and it relates a lot to the Constance Kamii article that James found last week on letting students play games to learn math concepts. Or Mike's idea of having students create their own math board games to play. Both of these ideas would hold so much math learning. I can only hope math returns to being taught through games. 
  
"You learn things by doing them and you remember what matters to you." - Piaget writes about math needing to be real in order for it to make sense to a student. This is the exact same reasoning. 

"It is far easier to test someone's knowledge of a pointless definition than to inspire them to create something beautiful and to find their own meaning." - Creating math journals with the students' own definitions forces them to own their mathematical reasoning and put it down on paper. 

"Be honest. did you actually even read it? Of course not. Who would want to?" LOL. This is hilarious because I read the paragraphs but all the math mumbo jumbo, I glazed over and kept reading at the bottom of the page. - OMG this page had me cracking up laughing because this was so me. Didn't even read it. Math's boring. Didn't interest me to read it. 

We make our 4th graders memorized a quadrilateral rather than just call it a four-sided shape. - Useless information and I completely agree that students don't need to know this. 


How do the arguments in the article relate (or do not relate) to your own personal experience with math as a student?  

"This rich and fascinating adventure of the imagination has been reduced to a sterile sets of "facts" to be memorized and procedures to be followed." - This is the math that I grew up with, memorization and procedures were how I was taught. 

"The cultural problem is a self-perpetuating monster: students learn about math from their teachers, and teachers learn about it from their teachers, so this lack of understanding and appreciation for mathematics in our culture replicates itself indefinitely." - This is true. I found this very hard during my first couple years of teaching. I struggled with understanding how to best teach my students in a better way than I was taught. The cycle repeats itself. 

"After a decade of being told they were "good at math," that in fact they have have no real mathematical talent and are just very good at following directions. Math is not about following directions, it's about making new directions." - This is where I laughed at my OWN situation. I was always "good at math" until I got to grade 11 and it started getting hard. I realized science started turning into math and I realized that I wasn't good at math after all. I was just told i was and it wasn't necessarily true. 

"I couldn't see, and then all of a sudden I could. Somehow, I was able to create a profound simple beauty out of nothing. and change myself in the process." - I love this concept. A lot of times, it takes me a long time to figure out the solution to a math problem, but when I do, and the light bulb moment comes on, it's an awesome feeling. 

"That's what math is - wondering, playing, amusing yourself with your imagination." - I've never personally thought of math as amusing or using your imagination, but I realize it should be. 

"What do they want me to do? Oh, just plug it in? OK." - This is my high school math classes summed up. Lol

"The textbook presents a set of definitions, theorems, and proofs, the teachers copies them onto the blackboard, and the students copy them into their notebooks. They are then asked to mimic them in the exercises. Those that catch on to the pattern quickly are the "good" students. - That was me. I was a "good" student that could write fast and understand the forum and plug in the numbers but never really loved math. 

How does the article’s arguments relate (or do not relate) to the experience your students have in your math class? 

"Do you really think kids even want something that is relevant to their daily lives? People enjoy fantasy, and that is just what mathematics can provide." - This is so true. Textbooks try gimmicks to try and make students relate to their content but it's forced and not applicable to their daily lives no matter how much they try and force it. It's more effectively to find math in your daily life and explore it, rather than force math in your life. 

"Math class is stupid and boring." - LOL. I've heard and said this exact same statement lots of times in the past. 

"Students need to be able to make their own definitions and say "my definition, my theorem, my proof." - Makes students take ownership of their mathematical reasoning. 

What is Mathematics?

What is Mathematics?

Math can take on many forms, many ones of which I've listed below. Depending on the situation, math can be both complex, yet practical; natural, yet abstract; unrelated, yet probable. To some, mathematics is a beautiful expression of freedom and to others, mathematics is a scary leap into the unknown and uncomfortable. However, no matter what your take on math is, we all must admit that it's an important part of our daily lives and without, our world would cease to run.