4. Art matters: Looking at mathematics through personalized projects

Art matters: Looking at mathematics through personalized projects

This we believe (NMSA, 2010).

* Educators use multiple learning and teaching approaches. Multiple Learning Approaches

My professional development plan includes integrating mathematics into the classroom using projects that are associated with academic content. This week my students have been taking finals for the third nine weeks. In the math class, every topic is tested on a different page. I coded the number of students who scored higher than 70 on each test and calculated the percent within each class for each of the topics. In addition, I found the overall average of the averages. Data are shared in the table below.

8^th grade topics n = 95

	Volume	Scatter Plots	Scale Factor	Composite Drawings	Transformations
Standard	77.3	86	82	78.2	82.3
Inclusion	58.2	69.6	62.1	63.6	77.5
Math I	84.1	92.6	87.1	81.7	N/A
Standard	75.7	79.1	55.8	70	86.4
Mean for All Classes	73.8	81.8	71.8	73.4	82.1

While we did projects associated with each of the topics listed, scatterplot and transformation projects had the highest personal connection and the highest amount of choice.

For volume, we examined how the volume of a cone and the volume of a cylinder with the same size base were related. This project involved water cups in the shape of cones, paper cylinders, and popcorn. In groups of three, students estimated how much popcorn cones could fill a cylinder. This activity also reinforces that relationship between the circumference of the base and the surface area of the cylinder. It allowed students to work collaboratively and I found them working quite well on the project.

For scatter plots, my students selected ten favorite foods they believed were healthy and ten favorite foods they believed were unhealthy. They researched the number of calories and grams of salt in each, created a spreadsheet using Google Sheets, sorted the data, created a graph of the data, then moved the data to Google Drawing to insert an estimated line of best fit. They saved the Google Drawing as a jpeg and inserted the image into a Google Doc. Finally, they reflected on their findings. This was an individual project.

For scale factor, students watched a great cartoon called “ScaleElla” from MathSnacks.com and completed interactive worksheets associated with the film. Based on the projects associated with these topics, scale factor involved the least amount of engagement. While it was entertaining, I was surprised the students did not retain more information.

Using Google Drawing, students created their own composite drawing and calculated the area. They also used graph paper to illustrate “nets” of the various polyhedrons. A guest speaker provided them with the training of how to use the Google Drawing tool.

For transformations, students had the choice to either create a dance that illustrated their knowledge of reflections, rotations, and translations or they created visual art of each of the transformations using colored pencils and markers. If they created a dance, they were able to work in small groups. The art products were all individual.

In algebra, we launched cannons (pom poms from straws) to illustrate quadratic equations and M&M rolls to illustrate exponential decay as a pre-activity to teaching them details about these types of functions. Illustrating quadratic equations was conducted in groups of four. The M&M activity was conducted in pairs. In both activities, students had to analyze their findings. Both were used to introduce students to quadratic and exponential functions. After the activity, one of my students said, “I really like that we actually do things other than just taking notes and practicing problems in math.” I tell you, art and engagement are wonderful tools for learning.

Advice

1.     I have had students create projects at home and on their own. What I find is that there are quite a few students who are not encouraged to complete work at home. For this reason, I include class time to work on parts of the projects so they can receive a passing grade for this part of the class.

2.     Student interaction and participation are tools that allow students to create information. The project does not have to be as detailed as the scatterplot experience, but it is important that the project relates to standards and their interests. I find that students love working in groups, but they do not always produce good work in that setting. (:

3.     Only one of the projects required students to use technology, but these skills will also help them when they get into high school. I have a teammate who allows them to compose writing using Google Docs and am thinking I will have my students create projects together.

4.     Be sure and monitor how students perform on assessments related to interventions. Even if you give a “unit test,” you can separate out how many students successfully completed that portion of the teaching.

5.     It is also possible to use projects to assess students’ 21st-century skills. Collaboration, technology integration, problem solving can all be assessed easily through projects.

4. Focusing on Art

4. Focusing on Art, Math, and Science

This we believe (NMSA, 2010).

*Educators use multiple learning and teaching approaches. Multiple Learning Approaches

“Class is already over?”

“I wish we could stay in here all day.”

“Can we do this again?”

“Help me!”

An inclusion teacher and I work together with one class of students. Our own professional development goal this year is to integrate more art into our classes. I found a wonderful book, “Arts integration and special education” (Anderson, 2015). Both she and I read it before Billy added his own comments.

  (This is Billy with remnants of what was shredded all over the floor.) The book is now art.

My teammate and I both believe and have research to support the importance, value, and impact art has on the spirit as well as the intellect of children and adults. How many of us started doing something in middle school (art, music, dance, singing, crafts, sewing, fishing, sports,…) that we either still love to do, or appreciate? So, she and I are on a mission to find ways to integrate art into the mathematics classroom so that our children see math in their world, experience math in their world, and learn to love math and art.

Students have participated in several projects that involve art and math: The mathematics of me; The math and art of place… This week students are working on a project called “The art, math, and science of what I love to do.” We started by researching what we love, and have created a giant timeline on the wall outside our classroom. We see the beginnings of our sports and interests.  

I presented a few examples: The art, math, and science of Bingo; The art, math, and science of origami. Next week we will look at the art, math, and science of snowflakes, tessellations, and fractals. For each topic I choose three points in time, provide a brief reflection of the math and the science, then share a product.

Friday, my teammate chose the art, math, and science of poinsettias. We were making poinsettias out of folded paper. We talked about what poinsettias are, where they come from, what makes them interesting (They are poisonous you know.) and we then followed directions to create them out of paper. Students measured, cut, folded; they examined fractions, midpoints, and angles. At the end of class our students gave us the ultimate feedback, “I wish we could stay in here all day.” “Woooohoooo!” was my teammates response. (:

I often think that our students need art as much as they need movement! These projects provided both.

Advice

1)   Find someone in your school who is willing to play. If you have ideas, sharing them will help ensure the development of better products.

2)   Think about how to use colored pencils, rulers, compasses, and protractors throughout the year.

3)   Give students opportunities to relate mathematics to their world.

4)   Display their work and allow them to reflect on the mathematics of their lives. (We are making a cookbook next….) (:

5)   This is the first one I am having them do during class. We work on a practice (review), develop a skill we are working on, then have about 15 minutes to work on their project each day. (I will let you know how it goes!!) (:

The Art and Science and Mathematics of Origami

The art of paper folding.

Timeline (Students must come up with three dates in history that relate to what they love to do.)

It is part of Japanese culture. In the late 1700s, were the first directions for folding paper cranes. 1797 The 1000 Cranes story is Japanese. It is also part of the Children’s Peace movement established at the end of WWII.

The 1950s, Yoshizawa Akira is considered the “father of modern origami.” He developed directions for describing how to make origami and he created a technique that uses wet paper to make softer lines. He received an award “The Order of the Rising Sun” in 1983 for his work. This is a Japanese medal of honor.

The following is a quote: “My origami creations, in accordance with the laws of nature, require the use of geometry, science, and physics. They also encompass religion, philosophy, and biochemistry. Over all, I want you to discover the joy of creation by your own hand…the possibility of creation from paper is infinite.” Akira Yoshizawa

For more information, go to: http://origami.about.com/od/History-Of-Origami/a/A-Brief-History-Of-Origami.htm

Mathematics (Students must compose a paragraph about how mathematics is involved in what they love to do.)

The mathematics of origami includes geometry, measurement, and following directions. Origami is based on circles and folds.

Science (Students must come up with a paragraph about how science is involved in what they love to do.)

I found a website by Robert J. Lang that focuses on origami in math, technology, and science. http://www.langorigami.com/science/science.php  On his website he talks about how origami was used while scientists were conceptualizing a giant telescope, a car company was designing airbags and the following picture that was used to conceptualize how light refracted in a laser. He also designs origami that uses software programs. TreeMaker is a program for drawing blueprints of origami figures that Robert Lang created. We can view one of Robert Lang’s designs at the following website: Diagrammer: Robert Lang’s Scorpion. The program lays out designs on square sheets of paper. See more at: hishttp://www.langorigami.com/science/computational/treemaker/treemaker.php

While looking further, I found what he calls “monumental origami” in which he creates life-size and larger art

In 2006, Lang gave a TedTalk on his work with origami in science and art. Student found his work amazing.I then found a TED talk by him. (This may be more appropriate for the teacher to build their background rather than for the students. I found it very interesting.)

http://www.ted.com/talks/robert_lang_folds_way_new_origami

Create a product (Students must create a product and share their findings with the class. They have 1-2 minutes.)

http://www.origami-instructions.com/origami-yoshizawa-butterfly.html  I made the butterfly using this website. It is based on Yoshizawa’s original directions. I use wrapping paper because it is easier to fold than typing paper.

We actually made origami butterflies. (:

“A true teacher is one who, keeping the past alive, is also able to understand the present” -Confucius

I found the following quote on Google. November 24 was Teacher Day in Indonesia.

Teachers are our mentors, friends, and catalysts. They’re the wild, eager sparks that can, with a word, set our passions ablaze. Not quite parents, they nevertheless raise us to be the very best versions of ourselves. And their impressions last lifetimes, as the lessons we’ve learned are passed down to others, like inheritances of wisdom. Today, let’s celebrate teachers, one of the noblest and most selfless of callings all across the world. http://www.google.com/doodles/teachers-day-2015-indonesia

Happy Teacher’s Day!

4. Reflections of the First Nine Weeks

Reflections of the First Nine Weeks: Structures and Resources

This We Believe (AMLE, 2010).

* Educators use multiple learning and teaching approaches. Multiple Learning Approaches

The first nine-week grading period ends Tuesday. It is hard to believe that I have been here for nine weeks. On the other hand, I feel like I have been part of this family my whole life. Some of my former university students want to get together. They will be student teaching in January. Prior to meeting with them, I decided to create a list of structures that worked for me this nine weeks.

a) Homework. I believe homework should reinforce what students know. I don't think students should do much on their own until they know enough of the basics to be challenged; if they keep doing things wrong over and over, it may reinforce bad information and bad habits. I give homework on Monday and it is due on Thursday. This allows my athletes time to complete their homework before a Wednesday night game; it teaches students to budget their time; and in my county, students can finish their homework before Wednesday night church. Because homework reinforces concepts, and stretches their knowledge, it is not dependent on what we do in class. I have been surprised at how many students are actually doing their homework. I chose one week each month to calculate the percent of homework completed. The following illustrates the percent of students who completed their homework on time:  August: 88%; September 81%; October: 62% 

Yay for August and September. Hmmmmm. I was at the middle school conference the week of October 7. I wonder if being gone influenced student participation?

b) Quizzes. I give quizzes every Wednesday. Quizzes are between ten and fifteen problems. Students have to show all their work. This allows me time to score the papers and prepare for remediation work on Thursdays, and allowing those who were successful to do enrichment - a modified version of "differentiation". It is called mastery learning and I find it very beneficial to helping those who struggle to get the remediation they need, and those who do not struggle to be able to learn additional content. So, after the first test, if a student failed, on the following Wednesday, the test included new material as well as previous week's content. If students successfully complete the previous week's work, with at least 80% accuracy, I move last week's failing grade up to an eighty. Those who are not successful (I have about eight EC (Exceptional Children) students who really struggle.) The lowest test grade they receive is a sixty.

c) Projects. This nine weeks, I gave two projects (Both are described at the end of this document.) The first project was to find real-life examples of slope (positive, negative, zero, undefined) for the standard students. The following is one of the pictures a student chose to illustrate a slope of zero.

Algebra students had to create a booklet or Power Point on what slope is and how to calculate it. The following is one of the pages from another student.

Slope is the steepness of a line on graph or stuff in real life. You can find steepness or slope by using y₂-y₁ over x₂-X₁.

The second project was called "The Mathematics of Me". There were three parts to this project. First, students had to choose a favorite number, tell why it is their favorite number, and give factors, prime factors, and multiples of the number.

My Favorite Number: Sample 1

            My favorite number is 210. This is because when I was in 3rd grade we had a candy corn guessing contest where you guess how many candy corn are in the jar. I guessed 210 and I was closest (there were actually 225) so I got the jar of candy corn. It sounds cheesy, but it was the first thing, that I remember, winning. Factors of 210 include 1,2,3,5,6,7,10,14,15,21,30,35,42,70,105, and 210, the prime factors are 2,3,5, and 7. Three multiples of 210 are 420, 630, and 2100.

My Farovite Number: Sample 2

My favorite number is definitely 16. This is my favorite number because when I am 16, I will be able to drive, date, and have a job. I will also be in my junior year of high school which means by then I would be in my 5th year of band.  

Next, they had to make a number line with 2000 in the center, mark three decades prior to 2000 and three decades after 2000. Their task was to write down three events that happened before 2000, three events between 2000 and 2015, and three events that will happen in the future - after 2020 (the year they graduate). The following example is from a student who loves to draw.

The last task was to choose three numbers that describe them, and tell why.

            “Three numbers that relate to me are 7, 24, and 2002.  The reason the numbers relate to me is because those numbers are my birthday.  I love these and I have known them for 13 years.  These numbers are also near my sister’s birthday and I will always remember these forever and ever, and I will never forget them!

I learned so much about my students. I learned of tragedies, ‘the year my father died;’ the birth of siblings, ‘bobo was born;’ their successes: “I met my bffs” (best friends forever) and their dreams: “I hope to go to be a teacher,’ “I want to get my license so I can get a job and help my family.”

d) Progress Reports. At the end of four weeks, I printed out their grades. Our state uses a program much like Engrade.com (a web 2.0 tool for recording grades). I gave them the following week to complete missed work. Those who completed their work, received partial credit for their efforts (I grade standard math students on effort; I grade algebra I for accuracy).

Today is the last full week of the first nine weeks. For the last two hours of school, we gave them time to complete any missed work. About twenty students were in my class diligently working away... Those students who had all their work completed, watched a movie about the Biltmore House (We are taking them to tour the Biltmore House in November). Interestingly, I had several students who didn't want to go watch the movie. They stayed in the class and read or worked on other things. In addition, three girls made pink and yellow ribbons for all of the team members for next week’s breast cancer awareness, “Pink Wednesday”.

d) Finals for the nine weeks. I haven’t always given a “final exam.” Usually, I just keep testing on Wednesdays. This year, I separated our final exam into four parts: expressions and equations, the meaning of slope, calculating slope, and for algebra students, Systems of Equations and for standard students, Pythagorean's theorem. Each part totaled 100 points and consisted of between 10 – 15 problems. The total number of points for the final is four hundred. The following is a breakdown of the average for each of the topics follows. As you can see, the average drops when students have to calculate slopes (standard students) and solving systems of equations for the algebra students. These skills will continue to be reinforced.

e) Students reflecting on the first nine weeks. Today I had students describe their comfort level on each of the final exam topics (A copy of the format is at the end of this document). I had them choose work from their folders, including this week’s finals. They had to choose samples of their successes or struggles with the content. I also asked them to evaluate their behavior for the nine weeks. Finally, I asked them to set an academic goal and a behavioral goal for the second nine weeks. Parent Night is November sixth. It is my hope that students will be able to share their knowledge using these resources. In middle schools, this format is called a "student-led conference".

f) Finally, seating charts are your friend. I find that moving students around breaks up the “dendrites”. (: haha;  I heard a session on ‘what connects dendrites’ last week. .. movement, language, art, music…). I find that when students get too comfortable, they begin to socialize more than focus. Moving them around breaks up their comfort level and allows them an opportunity to pay closer attention. On Wednesdays, I always move the desks into test formation (rows); on the other days students are in groups of two, three, or four. Note: I have found that my lowest students need a lot of structure, and so while I move students around, I try to keep these students in the same place.

Resources

Slope Project

You are to create an illustration of four types of slopes: positive, negative, zero, and undefined. In addition, you are to write an equation for the slopes you find using y = mx + b (slope-intercept form). A sample of this was when we drew images of the flag pole, the hallway, the steps, and the path to the soccer field. You may create this in a booklet form, a brochure form, or a powerpoint using images you take photos of.

The Mathematics of Me Project

This week we are looking at real numbers. There are three parts to the project:
1) (Whole/Natural) Choose a number you love "my favorite number" and tell why it is your favorite number (one paragraph). Include factors, prime factors, and three multiples of your favorite number.
2) Create a timeline (integers) to illustrate decades on either side of 2000
-30 - 20 - 10 0 + 10 + 20 + 30
On your timeline include (in words and illustrations) the following:
3 events that took place before 2000
3 events that have taken place between 2000 and 2015
3 events that you hope to take place after 2020
3) Choose 3 numbers that relate to you. Write a paragraph describing how these three numbers relate to you.

Rubric: All three are complete and illustrated (10); Most are complete (9); Some are complete from each section (8)
Turn them in by the 8th.

First Nine Week’s Reflection Tool

Dear __________________ (Put the name of the person who would want to see this.)

During the first nine weeks we studied seven topics. For each topic I have shared how I did. Attached to the document are examples of my work. If I struggled, I have shown how I corrected it. On each document, you will see what I know.

I have added notes to each topic to give you information about how we show our work.

For each topic I have rated my understanding with an

Excellent, Good, Okay, Need Work

Topics:

________________  My Ability on Evaluating Expressions

Expressions – this is where I have to be able to substitute a number for a letter such as x = 7 in the expression  3x means   3 * 7 which is 21.

________________  My Ability on Solving Equations

Equations:  Solving equations are very important in the math world! The equal sign separates variables and numbers. Our job is to combine “like terms”, use opposite operations to get variables on one side of the equal sign and numbers on the other, then to use opposite operations to solve for the variable. Here are four samples:

3n =  24                  2w  +  7  =  21               3(x + 4)  =  32            2x – 4  = 5x  +11

________________  My Ability on Identifying the Slope of Lines

We then studied the slope of a line: Positive, Negative, Zero, Undefined.

(Students will add images.)

________________  My Ability on Calculating Slope

We are able to calculate the slope of a line using right triangles and using an algebraic expression (y₂ – y₁)/(x₂ – x₁).   Look at the following example using the ordered pairs  (4, 2)  and (-3, 5)

(Students will add images.)

________________  My Ability on Calculating the Equation of a Line given points, slopes, y-intercepts

Next we looked at lines and slopes to learn how to calculate the equation of a line. Every straight line as a unique equation  y = mx + b  where m is the slope and b is the y-intercept.  Here is an example:

(Students will add images.)

________________  My Ability to Solve Systems of Equations

We also looked at solving a system of equations. A system is when there are two lines on a graph. The solution is the point (an ordered pair) that makes both equations of the line true. We learned how to do this by:

Graphing

Substitution

Elimination

(One way we did not learn is with Matrices… more to come on that.)

________________  My Ability to use Pythagorean’s Theorem

Finally, we are looking at solving for distance and midpoints of lines using

Pythagorean’s Theorem.

(Students will illustrate this concept.)

The following is how I would rate myself regarding

___ Paying attention in class

___ Participating in class without disrupting others

___ Doing my homework regularly

___ Studying for tests.

My goals for the next nine weeks:

·      Academic Goal:

·      Behavior Goal: