Chapter 3 Reading

Chapter 3 Reading: Culturally Responsive Teaching in Diverse Classrooms

            As I began to read this text, I had the precursor in my mind of how I am confident that I will embrace diversity in my classroom. However, it is difficult to understand how to do this, or what this looks like. I also hadn’t fully understood what types of obstacles exist, which would prevent me from doing this. This chapter begins by presenting how a variety of languages and cultures are gifts in the classroom, with a variety of perspectives and ideas to create a rich and vibrant classroom environment. However, many of these students struggle with literacy and learning, and as a result, they are placed in low ability groups and are limited because of this obstacle. Then the strengths that can come from instructional situations with diverse learners never occur because of the restrictions placed on them. Thus, my purpose for this reading was to find several practices that I want to implement in my own secondary mathematics classroom in order to embrace diversity and help bring down barriers.

            The example of how a science teacher embraces diversity in his classroom gave numerous examples how he provides the learning environment for ELL students to be successful, and for students of all cultures to be embraced and add interest to the class. I thoroughly enjoyed this example and aspire to have a classroom like Tim Fitzpatrick’s. First of all, I enjoyed the activity that he used at the beginning of the year to develop a learning community that fosters discussion, and not regurgitation of facts. The activity was for students to create autobiographic sketches and share aspects of their life stories to one another. This is something I want to use with my diverse classroom that I will be teaching at Breakthrough Saint Paul this summer. I believe this will be a good activity for the first day. Students can be creative, and then describe themselves through pictures and words. Many teachers believe that these types of activities take too much time, however, they can create a learning environment that fosters beneficial classroom discussions that may not have occurred otherwise.

To provide aid to ELL students, he labels all of the tools. If there are ELL students in my classes, and this appears to be beneficial, I believe that labeling items around the room and integrating a second or third language into the class at various times is a feasible step for me to take. I have a minor in Spanish, and very much enjoy learning parts of other languages. This could be crucial in the comprehension of key concepts in a class. A student can entirely miss an objective because of a language barrier; thus, I will take steps to avoiding this.

            Another way in which, Tim Fitzpatrick, the High School Science Teacher embraces cultural diversity is to undergo studying scientific problems occurring around the world. Relating this to mathematics, I was thinking about how students could dip into statistics from other countries, and then develop mathematical understandings of topics regarding countries around the world. This could be a statistics project that allows students to use the transitive approach, which would allow the students to do statistical analysis (think critically) and then generate conclusions and opinions. I also would like to have posters of mathematicians from around the world, hanging in my classroom, as well as infrastructures with beautiful geometries. I believe that classroom decorations can also provide a wonderful opportunity to passively display how important fresh ideas of all cultures can be in a classroom.

            Mr. Fitzpatrick also is selective on the passages that he assigns students to read. It may only be a couple paragraphs, and he will even rewrite material for more clarity, and assure that the key concepts are dissectible. He states that he likes to keep it real. He places emphasis on portraying key concepts in the most simplistic ways possible. I think that it is important to be precise. If there is a key concept that you want to assure it portrayed in math or science, it isn’t beneficial to assign an enormous amount of text that may have a lot of additional fluff and difficult vocabulary. Clear and precise text is important for ELL students, and all students.

            I also believe that the idea of getting family or community members into the classroom to discuss their professions is an awesome idea. Activities like this can be memorable, and help students apply the material they are learning in class to the real world, and what they may want to do in the future. The idea presented in the text is to bring in a carpenter to discuss trigonometry, and possibly have them create a small frame. It would also be a good activity for students to devise the questions to ask the community or family member. Having those formulated ahead of time can assure good questions will be presented, and creating these can be an activity in itself involving research. Then there is reading, writing, speaking, and viewing all involved is learning. I really enjoy this example because it gives a clear example of how I can involve families, as these relationships are important.

            What sticks out as most concerning for me, is the amount of ELL students that are placed in lower-track classrooms. As many people may have seen the popular movie staring Sandra Bullock, The Blind Side, I have heard the same story from one of my current Mathematics Pedagogy Professors. Some students are unable to read the assessments set before them, and as they fail to have success, it may appear that they do not understand the material. However, once the assessment is read to them, they are able to describe their understanding. Thus, I will do my best to have numerous types of assessments, projects, and activities that will allow all types of students to display their understandings. It can be so easy to look past the idea that the student may still understand the concept even if they do not do well on the test, as we rely so heavily on students’ ability to read successfully. It is so important to have relationships with all ones’ students, and understand their learning, and what needs to be done to assure the best learning experience possible.

Content Area Resource Collection

Taylor Berg

Jessica Crooker

EDUC 355

19 March 2012

Data Analysis and Probability: Data Representations (Bar Graphs, Histograms, Pie Charts)

Resource Collection for Middle School Mathematics

Resource 1: Professional Organization

http://scimathmn.org/stemtc/frameworks/742-circle-graphs-and-histograms

"7.4.2 Circle Graphs and Histograms | SciMathMN." 7.4.2 Circle Graphs and Histograms | SciMathMN. N.p., n.d. Web. 18 Mar. 2013.

What?

This is a website link to the detailed descriptions of all Science and Mathematics standards throughout the grades. This is created by the Minnesota Department of Education. I found the particular 7^th grade standard of Data Analysis which states, “Students in 7th grade have been using different displays to show data they have collected. They have used bar graphs, line plots, line graphs and double bar graphs. They will move into circle graphs and histograms in 7th grade, finding a part of a circle (sector) given the percent or other data for the section. They should be able to determine missing values of a circle graph. They will transfer the data into displays to show the data. They will use the information gathered or make a frequency table to help them in the display of the data” (Standard 7.4.2 Essential Understandings).

So What?

This is an extremely beneficial site for mathematics and science teachers to reference. All standards and specific benchmarks are explained thoroughly. Associated with each standard, there are also common misconceptions, vignettes, instructional notes and resources, ideas for differentiation, example assessments, and resources for parents and administration. This site is packed with information and resources for each specific standard.

Now What?

I would love to reference this site regarding all the various units I begin. There are links to websites that are relevant and could be utilized. Particular problems from the assessment examples could also be used in class, or on tests or quizzes. I also find the common misconceptions extremely beneficial to see as I go into my first years of teaching, and it is difficult to anticipate how students will respond to particular material. This can help in preparation.

Resource 2: Website

http://illuminations.nctm.org/ActivityDetail.aspx?ID=204

"Data Grapher." Illuminations:. National Council of Teachers of Mathematics, n.d. Web. 15 Mar. 2013.

What?

This website allows students to enter data and then analyze the data using bar graphs, line graphs, pie charts (circle graphs), and pictographs. Multiple sets of data can be entered and then one can pick which sets to display in whatever representation seems most fitting. I found this site as a listed resource from the source above, and the National Council of Teachers of Mathematics created this site.

So What?

This is a wonderful way to have students work with data and decide which method of representation is best. In addition, students are working with technology, which will likely be engaging for students that spend so much time on their phones and computers. It is important to incorporate technology, as this is what is interesting and familiar to them.

Now What?

I would love to use this as a mathematics project. To even further engage the students, I could allow students to enter data they collected themselves, or that they found. There are always better results when students have choice in the material that they are working with, and this could allow them to truly pick data that is interesting to them, and relevant to their lives.

Resource 3: Children’s Book

The Great Graph Contest by Loreen Leely

Leedy, Loreen. The Great Graph Contest. New York: Holiday House. 2005. Print.

What?

This children’s book is about a toad and a lizard that are in a competition to create the best graphs. Throughout the story they are trying to create better graphs than the other and incorporate bar graphs, pie charts, Venn diagrams and quantity graphs. There is also a snail that is judging which graphs are the best, as well as giving helpful reminders to use labels and such.

So What?

Although it is a children’s book, there are many helpful lessons that middle or high school students can benefit from. For example, students of all ages have the tendency to forget about the importance of labels. A graph does not have a lot of meaning when there is no way for knowing what it is representing. There are many effective examples of representing data in a variety of methods. This helps demonstrate of applicable mathematics is, and how math is everywhere! J

Now What?

This book could be used as a fun introduction to this unit. It would also help students spark their own ideas of what they could use as data for their own Data Analysis Project, and then what different graphs would best represent it. The characters of the book often ask, “Can you make a graph about that?” which helps emphasize that such a variety of data can be represented on graphs. The snail that is judging which graphs are the best can help indicate that certain data is better represented on particular graphs more than others.

Resource 4: Chapter Book

Charts and Graphs: Microsoft Excel 2010 by Bill Jelen

http://www.barnesandnoble.com/w/charts-and-graphs-bill-jelen/1100306197?ean=9780789743121

Jelen, Bill. Charts and Graphs: Microsoft Excel 2010. Indianapolis, IN: Que, 2011. Print

What?

This book is filled with chapters of information of how to communicate information clearly through Microsoft Excel graphs and charts. There are step-by-step instructions, case studies, and links to YouTube. The step-by-step instructions are broken down and clear to follow in order to create designer quality graphics to represent data.

So What?

As I majored in Mathematics, I have friends from my courses that have finance or actuarial science internships that rely heavily on Excel. I have heard numerous times that they wish there had more exposure and exploration with Excel in their coursework, or throughout their education experience. This book provides numerous examples and explanations on how to use various Excel functions for data analysis and representation, so as a teacher; I need to find instructions or examples that would be appropriate for my classroom.

Now What?

I could have this be an activity that I provide a lot of scaffolding with hold to read the instructions. It would be manageable for students if I found one set of instructions from the text, and then made photocopies. I could even find several different sets of instructions, so each small group could tackle a different graph or chart on Excel. This technology project is so applicable to the work force; it would be awesome if they could be organized in groups according to their interests of what they want to do when they’re older. Then I could provide data for each group accordingly. Any exposure to computer programs like Excel is so applicable and transferrable into “real life”.

Resource 5: Comic Strip

http://search.dilbert.com/comic/Pie%20Chart

"Pie Chart." On Dilbert.com. N.p., n.d. Web. 18 Mar. 2013.

What?

This is a silly cartoon, which emphasizes how data represented neatly in pie charts looks important and worthy of ones’ time to look at! Pie charts can allow information in the workplace to be clearly represented and then easily presented and understood by others that need to grasp the meaning of the data. Well-presented and represented data may also appear convincing when it needs to be as well.

So What?

This comic is relatively funny, and then also extremely relevant to the unit. This could be used in various ways in the classroom and then help students to think about how important and effective well done representations of data can be!

Now What?

 I have had teachers that would place little comics on tests or quizzes, and it provides a nice environment, and brief relaxing moment, prior to a stressful situation. I could also have this on an exit or admit slip, and have the students write a reflection on the cartoon and what they can take from this. (I will have to talk about how I know that everyone always has something useful to say, but this is just Dilbert being ill prepared at work, but knew that graphs and charts are extremely important to convey the meaning behind data J )

Resource 5: YouTube Video

http://www.youtube.com/watch?v=lVlXbH4nczI

"How To...Draw a Simple Pie Chart in Excel 2010." YouTube. YouTube, 01 Oct. 2010. Web. 18 Mar. 2013.

What?

Dr. Eugene O’Loughlin from the National College of Ireland gives an extremely clear YouTube demonstration on how to create Simple Pie Charts on Excel. He uses a basic example of amount of apples, oranges, pears, and bananas that are sold over four quarters. Then he shows how to put two different quarters of sales into pie charts to clearly compare the amount of each fruit sold during those two quarters. Then he shows how to make the pie charts three dimensional, which is more visually appealing and easier to understand.

So What?

Dr. O’Loughlin speaks clearly and slowly while explaining how to approach the creation of the pie charts. He also uses a curser that is a big red dot, which is easy to follow where he clicked, and then what happened after. The video is also a brief four minutes, and filled with a feasible amount of information to grasp. He makes two flat pie charts, and then makes then 3D. 

Now What?

This is a wonderful instructional video to teach students how to create these pie charts. It would work well to watch this on a projector in the computer lab, and have the ability to pause, and allow the students to go through each step along with the instruction. It is advantageous to integrate technology, as well as to hear a different voice of instruction. Dr. O’Loughlin has an interesting, but understandable, Irish accent that the students may also enjoy. (March may be a fun time to do this lesson! J )

Resource 6: Website

http://www.ixl.com/math/grade-7

"Seventh Grade." IXL - Math Practice. N.p., n.d. Web. 18 Mar. 2013.

What?

This website contains numerous example problems associated with all the standards across the grade levels. I was able to choose the seventh grade level, and then locate the subheading of Charts and Graphs, which is one of twenty-seven topics for seventh graders. Then below the headings are more specific subsets of that topic, and once you click on those, there are example problems that one can answer and receive immediate feedback from.

So What?

This website is extremely organized and easy to navigate. I went through and did some of the example problems, and they’re directly aligned to the standards. The immediate feedback is wonderful, and the problems even increase in difficulty, as you’re successful. The problems involve interesting information and are bright stimulating problems. This could be an interesting way to practice the material. Especially because it is so simple to generate the exact type of problem a student may need. If certain students are struggling on particular topics, it would be easy to differentiate the activity using this website, and assure that students are receiving the practice on exactly what they need.

Now What?

There would still need to be a few things that I would need to consider prior to using this website for practice. I would want to be able to see how the students do with the problems, or establish some sort of goal. I’m not sure that just doing a bunch of practice problems with the time allotted would be that intriguing. It could maybe be something I project on the wall and have the entire class work on the same problem, working in small groups, and make it some sort of review game. I could also have this site as an option to go to with time left over after working on an assignment in the lab.

Resource 7: Website (s)

Exploration of Histograms v. Bar Graphs

http://illuminations.nctm.org/LessonDetail.aspx?id=L812

"There Is a Difference: Histograms vs. Bar Graphs." Illuminations:. N.p., n.d. Web. 18 Mar. 2013.

http://mathcentral.uregina.ca/QQ/database/QQ.09.99/raeluck1.html

"Bar Graphs and Histograms." Bar Graphs and Histograms. N.p., n.d. Web. 18 Mar. 2013.

What?

The first website listed is another resource from the National Council of Teachers of Mathematics. They have many resources available for teachers to utilize in their classroom. This link provides a lesson plan, which helps with differentiation of Bar Graphs and Histograms. The lesson involves collecting data on presidents, from three links provided, and they can choose which link to go to. Thus, there involves some choice, which is crucial to interest students. However, it keeps the students focused and using data that will be effective for their understanding. The students will collect data and make frequency tables and then graphs involving the presidents’ political party (bar graph for categorical data) and then the inauguration age (histogram for numerical data). I also found a link from Math Central, where a student provides an explanation and example of the difference, which is rather clear.

So What?

As these two graphs are visually very similar, it can be confusing for students to understand and remember the difference between the two. I believe that making both of the graphs using one topic, will allow the students to clearly compare and contrast the two types of data representations. The students will also see how the histogram can be pushed together into one fluid graph, and it does not work that way with a categorical graph, or a bar graph.

Now What?

I would love to use this lesson in my own classroom. I believe this project could work well in groups of two. I believe partners would be especially effective with the data collecting, as one student could be navigating the computer, and the other could be recording the information into the frequency table. As far as the other website link, I believe it may be nice for students to have that as a handout to read through, or I could mirror this type of journal entry in my class. Students could write a journal entry reflecting on the different and creating an example, after they have gone through with the completion of the President Project.

Resource 8: Poem with Visuals and YouTube Presentation of Poem

Florence Nightingale: The Lady with the Pie Chart by Andrew Porter

"Inkpotamus." Florence Nightingale: The Lady with the Pie Chart. N.p., n.d. Web. 18 Mar. 2013. http://www.inkpotamus.com/content/florence-nightingale

What?

Above is a picture of the last stanza of the poem “Florence Nightingale: The Lady with the Pie Chart”. It appears to purely be a historical poem, and then at the end begins to also be a mathematical one. This poem describes how a graph or chart is important to present information in an interesting manner that is clear to an audience.

So What?

This also allows students to think about graphs in a historical context. It is always beneficial for students to see mathematics applied in all sorts of ways. This poem is historical, as well as an interesting piece of literature, as the rhyming allows it to flow and adds interest. 

Now What?

Depending on how much time one wanted to spend with it, this poem could be used in a few different ways. The YouTube is interesting with all the images, so it may be something I could play at the beginning of the class hour as an attention getter. Students could also read it on their own and in a group and then highlight what this tells us about graphs and charts. What does this poem tell us about their importance?

Write to Learn Mini Lesson

Reflection on Write to Learn Mini Lesson:

My writing to learn activity was a writing break. I wanted to have students hear the name of the theorem and first think about what they are looking to discover. Then I wanted to an activity to discover the Triangle Angle Sum Theorem, and then reflect on the discovery by putting it in ones’ own words. In my preparation, I decided I was going to use an activity of manipulating a triangle to do a physical proof of the theorem. I used this activity with my kids last summer and they loved it. I took time to practice, and essentially script, my mini lesson. I wanted to make sure I demonstrated each portion of the mini lesson, but still kept it to five minutes. I also took pictures of each step of the activity, in order to create the step-by-step directions. Last summer, I simply demonstrated the ripping, but then orally told them to place the vertices together. I felt prepared prior to my lesson.

There are definitely things I would change, but there were also some positives of my mini lesson. I think that a lot of people enjoyed the hands on activity, and then time to reflect on it afterwards (although that was kind of cut short!). If I could do it again, I’m not sure I would’ve had the writing break before the activity. I would’ve maybe just had them go into discovering how many degrees are in a triangle, and then let them know the theorem that they just proved to themselves. I wanted students to get into the mindset of what they were looking for, but I’m not sure if it was as effective as I wanted it to be. I also could’ve modeled how to write ones’ own definition or discovery. I wouldn’t want to write out an entire definition of the Triangle Angle Sum Theorem because I wouldn’t want mine to be copied down. I still want the students to reflect on their discovery and formulate their own, and not simply copy mine.