Social Justice Lesson

Green Corn Puzzle Social Justice Lesson - (This is designed as a Notebook file so this format isn't nearly as interesting or complete because there are no interactives available in Blogger like there are in Notebook.)

Specific Expectations

Social Studies - Mapping

Math - Patterning & Measurement

The Arts - Visual Art

Native Language & Culture

Timeframe: If done properly, this lesson should take an entire day. Examples and introduction can be done early in the day to get students involved in "Minds On" activities. Also, depending upon their painting skills, this portion could even extend into the next day. Be prepared for frustration. This lesson is not easy. But it's so worthwhile and lots of marks can be assigned because it's cross-curricular.

Note to Teachers: This is designed to be a cumulative lesson to be completed at the end or near-end of having taught all of these previous curriculum lessons. 

Also, since this lesson is designed for Six Nations students, I chose to use Six Nations and surrounding area as the example of scale using a map (plus, the maps are free which always helps). 

For the visual art portion of this lesson, I chose to use the theme of Green Corn since it plays a vitual part of Rotinonhson:ni culture. 

By having the students see themselves in the educational learning and curriculum, it helps them to relate and identify with the material being taught and it has a longer lasting impact. 

Lesson Overview 

1. Review the importance of Corn to the Rotinohnson:ni from our previous lessons on the Ohenton Karihwatehkwen and lessons on Green Corn ceremonies. 

2. Review what is scale? 

3. Read definition from math text. 

4. Observe Six Nations map.

5. Green corn puzzle introduction.

6. Activity time! Start planning, then start painting. 

Materials: 

-Grade 5 social studies text (or any text that has examples of scale)

-24 Six Nations maps (these can be obtained for free at Six Nations Tourism or any Six Nations Parks & Recreation building) 

-Green Corn Puzzle instructions handout 

-coloured and black & white photos of the puzzle

- teacher sample square (draw and paint a sample square)

- 16 squares the same size as teacher square

-16 individual student grids, calculators, rulers, scissors, paint, paint brushes, palettes (styrofoam plates), palette knives (plastic butter knives)

-8 wash cups for brushes 

Note: Depending on the number of students in your class, you will need to create more or less sample squares since the corn photo must be divided into equal square parts ie. 4x4=16 or 5x5=25. This makes it easier for grade 5 students to divide. (Even though it could really be divided into anything but that would be a nightmare!)

Instructions:

1. We will be creating a Green Corn Puzzle using social studies, math, and arts skills.
2. Explain what our day’s project will be by going over the specific expectations required for their assessment. (Show the following 2 slides then continue with lesson.) 
3. Check out the following blog for further lesson explanation. http://www.mrsbrownart.com/5th.htm  
4. 
   1. 
      
   2. Can anyone tell me what scale is? 
   3. Read scale definition in grade 5 social studies text. 
   4. Compare Maps at Different Scales. Have students notice the 2 different size maps of the Great Lakes as 2 examples of scale. One small, one blown up bigger. 
   5. Direct students to look at their map of Six Nations back page to enlarged photo of South Western Ontario. Point out how the lack of detail in Btfd and SN. Our estimated scale for this map could be 1cm=50km
   6. Flip map over to compare it to the map on the left and notice that there’s more detail to Btfd and SN. Our estimated scale for this map could be 1cm=5km
   7. Ask what the 2 road names we can see in Btfd (Erie Ave and Colborne Street). Our estimated scale for this map could be 1cm=1km
   8. Direct students to find both roads on the above map and notice how there’s even more detail as the map gets smaller in scale.  
   9. Redirect focus to Btfd/SN map and notice the shape and colour of SN. Compare that to the enlarger map of SN and notice how there’s even more detail in map because the scale is getting smaller. Our estimated scale for this map could be 1cm=0.75km
   10. Turn map to the back to see how the map of Ohsweken is the smallest in scale and has the most detail. Our estimated scale for this map could be 1cm=100m
   11. 
       
   10mm=1cm
   100cm=1m
   100m=1km
   
   
   1. 
      
   2. 
      
   3. Explain we will be doing the same thing with making a small scale bigger only instead of enlarging a map, we will be enlarging a puzzle one piece at a time. 
   4. 
      
   5. Each student will be responsible for creating one piece of our 16 piece corn puzzle like I have done. 
   6. 
      
   7. You will start by continuing to divide your graph from it’s current 4x4 stage and turning it into an 8x8 graph.
   8. 
      
   9. Demonstrate how to divide your page into a graph: Who can tell me what is the length and wide of your paper in mm? What is a quarter? If I wanted to divide my paper into quarters what would I do? Sixteenths? Have students divide their own pages into sixty-fourths. 
   
   
   Math Minds On

   1. What does each fraction look like?

   2. What is the pattern for the fractions?

   3. Measure each section of the grid. How many mm is a whole page? 

   4. Using your calculator, how would I figure out how much is a quarter of a page? Sixteenth of
   a page? Sixty-fourth? What is my pattern for finding the measurement?

   
   

   You might get handed the black and white version of the top left corner piece and that is what you have to recreate. Or you might get the bottom right corner piece. It's up to you to recreate your 1" x 1" small square, black & white puzzle piece and enlarge it onto an 8" x 8" square of paper and then paint it accordingly. 

   
   

   Painting your puzzle piece

   
   

   Also, be aware of which colours you choose to mix. If you make a blue green and everyone else uses a yellow green your piece will stick out. 

   
   

   Shade: a colour, especially with regard to how light or dark it is or as distinguished from one nearly like it : various shades of blue | Maria's eyes darkened in shade.

   
   

   Tint:  a shade or variety of color : the sky was taking on an apricot tint.

   
   

   Wash: a layer of dilluted paint spread thinly on a surface : the paper was covered with a pale lemon wash.

   
   

   
   

   1.  If I wanted to make my green darker, what colour would I add?

   2. If I wanted to make my green lighter, what colour would I add?

   3. Using your palette, palette knife, and paints, experiment mixing different shades of green and
   yellow. 

   4. When you think you've found the correct colour, begin painting your square carefully. 

   
   

   ***REMEMBER YOU CAN ALWAYS ADD MORE PAINT BUT YOU CANNOT
   REMOVE WHAT YOU'VE ALREADY PAINTED!*** 

   
   

   
   

   
   

   
   
   
   

Monster Math Night Review

Monster Math Numeracy Night

In reflecting back upon OMSK’s Monster Math Numeracy Night, I’d have to say it was the best one we’ve hosted so far. This was our fourth year hosting this event and each year it gets bigger and better I believe. 

The event ran from 5-7pm on Thursday, October 30th. A spooky menu was available for purchase from our Home & School Committee, which encouraged more teachers to stay and have dinner at school and then host a math centre. 

We requested $300 from our Home & School in the past years and did so again this year. Our Home & School president, Lana Martin, gladly sponsors the event because she makes that amount of money back and more from the sales of her dinner. The money we borrow is used to purchase all of the small prizes that the students can purchase with their “monster money.” Prices ranged from $0.25 to a couple dollars for items. Students had to do additional math to count out the correct money amounts to “purchase” their prizes. It was also used to purchase larger prizes for the family door prize (Cineplex gift certificates, popcorn, and a movie basket).

At last year’s event, we hosted over 300 people (families, students, and guests) throughout Numeracy Night and this year was about the same. Last year we only had 5 tables set up with teachers who participated in the event because most of the teacher doubled up and ran one table together, which took away from the number of games available to play. This was a concern because students’ feedback was that the event was fun but they wished there was more games to go to. We wanted to improve upon this for this year and were able to by having double the math stations for students to play. 

New this year was the addition of a haunted stage, which was the hard work of Mrs.Deb Martin-Able’s math resource students. They spent the week leading up to Numeracy Night brainstorming ideas for the layout, making the props, and decorating the stage. While I wasn’t able to go through the maze on Numeracy Night since I was so busy running my own thing, the screams of terror from the kids echoing down the hall leads me to believe that it was a success. :) Each math student wore a scary costume and was hidden throughout the maze and would jump out to scare the students going through the maze. In order to pass, the student had to answer a math question generated by the math student and they were allowed to continue to the next monster and math question. It cost $5.00 to enter the monster math and the students enjoyed playing more math games in order to raise enough monster money do go through the maze numerous times.

The pride of the math resource students was evident while they were busy setting up their stage. Afterwards they received lots of compliments from their peers and teachers on what a great job they did. This was extremely beneficial to their self-esteem especially since these are the students who are usually the ones who need help. Instead, it was their night to shine and they definitely did. 

Another new addition was the community raffle in order to raise money from OMSK to donate to Teiehkwa and her battle with cancer. Prizes were generously donated by OMSK staff. In total, we were able to give Teiehkwa and her family almost $400. 

The last new addition to Numeracy Night was having the Scholastic Book Fair overlap with math night. This was a amazing way to get students excited about both numeracy AND literacy. In that first day we had almost $2000 in sales, which was a great push to being able to add $2200 in books to our school classrooms and library. I was in charge of running the book fair so as students came in, I had them estimate how much their books would cost and then we’d total them up and see if they were close. We will be overlapping both events next year as well as a way to push literacy and numeracy and make them both fun. 

I was so busy with my own events that I wished I had more time to actually get into the math night and see it in action myself. I came in at the end when things were winding down and it looked like the students were having so much fun. 

I organized two math centres in the library that were mathematical skills but about literacy. I had 4 different stacks of b  ooks for the early primary, primary, junior, and intermediate. Each group had to estimate the number of pages in their age group’s stack of books and put their name on it and enter it into our draw. One student from each category who estimated the closest to correct number of pages each won $15 of free books. The second centre I did was a spinner which different book covers on it. It was based on probability. It had two different spinners (one for primary and one for junior/intermediate). Questions for example could be: 1) What’s the fraction of books that have yellow covers. 2) Write 2 different equivalent fractions that represent the number of books written by Robert Munsch. 

I was able to run my math centres for part of the night; however, I quickly became swamped in the Book Fair sales so my partner had to take over at helping run the 2 math centres. Next time, I will bring 2 volunteers to help me with the centres and the book fair as well. 

Overall, upon reflecting on this night, the only thing I can recommend it having more math centres. Although we did have double the centres from last year, this event is so big that even that was not enough. A suggestion could be to invite parents/guardians and the grade 7 & 8 students to create and run their own math centres to add to the night. I look forward to what we come up with for next year. 

Social Justice & Mathematics Personal Response

Social Justice & Mathematics

Sumona Roy was our guest speaker for the night and gave us many different ideas to incorporate math into other areas of the Ontario curriculum with specific reference to social justice and mathematics combined together.

Minds On - Waste Art 

Sumona taught us to incorporate social justice and the environment into our regular mathematics lessons in order to promote student engagement. Lots of students love talking about social justice but aren’t as fond of math. The trick is to get them into liking math through expiring the theme of social justice. She used her website: http://socjusmath.wikispaces.com/ to show us different Minds On activities that included the different zoomed in photos of pollution and recycling waste and how the mathematics is absolutely amazing behind how much waste we throw away each year, month, day, hour, and even minute! I can’t wait to show this to my students when I’m back teaching mathematics one day. 

Principles for Teaching Social Justice

Principle 1: enable significant work within communities of learners - if you engage students in meaningful work, you’ll have engaged students in mathematics. When you make the math real and bring it into their world is when the most learning happens. 

Principle 2: build on what students bring to school with them - knowledge and interest, cultural and linguistic resources - all students have talents and are knowledgeable or have a passion in different areas. It’s up to you as their teacher to find their passion, find out what their background is and run with it. Use that to capture their attention in teaching all areas, not just math, and you’ll have students who want to learn more. 

Principle 3: teach skills and bridge gaps that your students bring with them - Knowing ahead of time that all students come into your class with gaps, helps you to get the balling going with finding out what their specific gaps are. Key Math and other testing forms like ONAP help with this.

Principle 4: work with (not against) individuals, families, and communities - these people are your best resource to helping you with teaching mathematics to students. You have your students for half of their day, parents have them for the other half. Getting their input and the community input on services already available to help you will help lessen your load and reinforce ideas already taught to students. 

Principle 5: diversify your forms of assessment - use different ways of assessment interviews, tests, show and share, art forms, etc to get a better idea of a well rounded student.

iPad Apps

Sumona also talked about using technology to incorporate mathematics with your students. Two different apps she mentioned as useful in her teaching are: 

Explain Everything and Educreations

Both of these apps are amazing for documenting student work and giving students the opportunity to tell you about their mathematical thinking. This is great for students who aren’t necessarily the best at writing their thought process but are better articulating their mathematical thinking orally instead. This way we can more accurately assess all students. 

Culturally Responsive Pedagogy

Culturally Responsive Pedagogy 

Page 3

What does a school look like, sound like and feel like when we promote reflection, honour the community and support authentic collaboration among staff, students and parents?

The environment of a culturally responsive school depends highly upon the importance that administration places on this valuable concept as well as what teachers and support staff do to ensure this is practiced at the school. Educators are aware of what it means to be culturally responsive and practice it in their daily interactions in the classroom and in the school environment as a whole. Parents and teachers display effective communication with each other that’s based on mutual respect. Administration and staff also display effective communication on both parts that’s based on mutual respect. Individuals are celebrated for their strengths and given assistance with areas they can improve on. With this in place at the top levels, students have a good model to follow in their interactions in the classroom on how to treat their peers. 

What does a classroom look like, sound like and feel like when it is inclusive and when instruction is responsive to the full range of student diversity?

A classroom where this is practiced is an inclusive environment where ALL students are able to share their ideas without fear of ridicule or rejection. Students see themselves in the materials that are being taught and can visualize themselves in their work. 

What further information would be helpful in considering cultural relevance and cultural responsiveness in our school?

All teachers of Six Nations schools need to have a strong understanding of the students and community they are working within. It is only when you truly understand the students you teach, that you are able to really get through to them. This can include the different religious practices some families follow, the different family dynamics that regularly occur on Six Nations, cultural lifestyle changes on reserve compared to off-reserve, how our students see themselves in their education (or not), etc. Speaking with seasoned educators, elders, and parents can help someone get a better understanding of cultural relevance in our schools. 

How do we work with our communities to help everyone appreciate the importance of culturally responsive teaching?

We can help other’s appreciate the importance of culturally responsive teaching only to those who WANT to learn. Unfortunately, there are people in our communities who are close-minded and do not want to learn so to say how to we help “everyone” appreciate the importance is not a fair statement. Everyone has to want to learn in order to learn. Some parents, staff, etc choose to remain ignorant - non-native AND native teachers included. 

But besides that, we can work with those who want to learn by giving some kind of sensitivity training to educators who aren’t as familiar with Six Nations. (In reality, I believe our teachers and T.A.s should already have this knowledge or at least familiarity BEFORE even being hired since it’s a HUGE requirement to be able to effectively teach on reserve, but that’s a story for another day.) 

What is the impact on our students when we do not acknowledge the complexity of culture and difference?

This issue is one I feel very strongly about. When our students do NOT see themselves represented in mainstream media, in their own education, in the teachers that teach them, we are doing a huge disservice to them. This is one of the reasons I choose to teach on reserve, so that our students can have a strong, native teacher to be able to be as culturally sensitive as possible in my teaching of them. 

I purposely use photos of onkwehon:we in my flashcards and Smart Board lessons. I use our hotinonhson:ni stories and games in my activities. I read stories of hotinonhson:ni or at the very least other First Nations when I’m trying to get a point across. I even use onkwehon:we figurines in my lessons on the words for family members versus using your standard “white family.” Lol. I go out of my way to make sure that my students see themselves represented in their learning; see themselves representing in the stories we read; see themselves in positions of power and success through examples I give. 

I go to longhouse and learn about our culture and traditions so I can more effectively speak about them and teach them to my students. I’ve went back as an adult to learn our language so that I can understand the complexities of it and be able to share it with my students. I am in a hotinonhson:ni women’s drum group and learn our songs and protocols about socials so I can teach them to my students. All of these teachings have changed who I am as a person and as an educator. I never had this knowledge growing up as a student on Six Nations and I always felt like something was missing in my life. I was always on honour role, did very well in school and university, got a good job, did everything I set out to do. But it wasn’t until I learned my language and more of my culture that I fully felt complete as onkwehon:we. 

I am so excited to share this knowledge with my students everyday to not only teach them the curriculum (which anyone can do), but to teach them how awesome we are as onkwehon:we people learning the same curriculum. We see things differently than mainstream society. We feel things differently. We process things differently. But we need to celebrate these differences not as being a bad thing, but as being what makes us unique and something to be proud of. 

When students aren’t taught about the complexities of our culture, and how awesome it make us, they suffer unnecessarily. Pride in their differences is what makes them unique and is what is going to make them persevere when things get hard in education or in life in general.  

Page 6

What questions might we reflect upon to examine our own biases towards diversity and cultural responsiveness?

In a PLC staff meeting, you could maybe begin by asking if staff even know what diversity and cultural responsiveness is. If you can’t even give a definition of what this means, that’s a good jumping off point to learning more about it. 

For those teachers who know, they can brainstorm and share with their groups examples of each so it’s non-threatening in sharing of ideas. Then the ideas and biasses can collectively be shared with the whole so no one is centred out as having that specific bias themselves. Then you can begin to start fixing those biases that come up in the staff. 

How would we start a staff discussion on moving towards cultural responsiveness in a more intentional way?

We could start a staff discussion by a couple staff members who are willing to demonstrate specific examples of what they do in their classrooms to be more culturally responsive to our students and share the results of these actions. I believe positivity fuels itself and it’s hard to not jump on board when other colleagues are sharing ideas of what’s worked for them and how well the students respond to the changes. It’s infectious and hopefully inspires other teachers to climb on board as well. 

How might we integrate specific life experiences of our students into daily instruction and learning processes?

I love doing this and students love hearing about their teacher’s personal life experiences in learning as well. When I teach about ceremonies, I tell them what I know happened at the Kanyenkeha:ka longhouse and ask the other students who I know go to other longhouses about what happened at their longhouse’s ceremony. For example, I can say that the turtles won the peach pit game at my longhouse for a certain ceremony on the weekend and all the turtles in the class cheer and are so proud and excited. But then, I always have a story to share that maybe at Onondaga longhouse the other clans won. Students really relate to the lessons when they see themselves in the learning. 

Page 7

How might we support students in making decisions about their learning that integrate who they are and what they already know with their home and community experiences?

Teachers can give the students one of those tests where students can see which type of learner they are: visual, kinesthetic, auditory, etc. We can invite students to share ideas on how they learn best to give them responsibility and a say in their learning. We can also involve the parents and guardians and even elders to discuss how we as onkwehonwe learn. This will give us background into where the students come from and their community experiences. 

How can we lessen dominant perspectives in our curriculum so that contributions from different backgrounds can be better understood and integrated into learning?

We can have teachers that know the difference between dominant perspectives and our onkwehonwe perspectives. Teachers must be knowledgeable and comfortable with knowing exactly who they students they teach are. This way teachers are able to easily use the Ontario curriculum but teach it using hotinonhnson:ni perspectives and values. When teachers don’t know this or aren't comfortable teaching it, they resort to using Western or dominant perspectives instead. If a teacher doesn’t know the grade 8 math curriculum, they must teach it to themselves or learn it before teaching it. It should work the same with teaching our students. It’s ok not to know. But it’s not ok not to learn. 

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.