Best Math Apps For High School Students Bad In Math Middle School Case Study

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Middle School Case Study

I met “Gloria” when I first went into my assigned observation classroom – 9th period Native American Connections. She is a 13-year-old seventh grader with brown hair and brown eyes. She is Native American. She is left-handed. She has one sister (16-years-old). She is not very tall, but is showing the first signs of puberty. I noticed occasionally that she wears light eye shadow (like white or pale pink) and lip-gloss

When I asked “Gloria” a few introductory questions, I discovered that her favorite subject is math, her favorite color is red and her favorite music is rap. “Gloria” is not involved in any clubs and doesn’t really watch television.

When I asked “Gloria” for her class schedule, she did not have a copy of it; but was able to tell me what classes she takes and when. She starts her day out with PRO-Time (People Relating to Others). Then for second period it’s on to reading. Third period is math, fourth period is Native American Connections, and then she goes to lunch at fifth period. After lunch is Language Arts for sixth period, science for seventh period, keyboarding for eighth period, Native American Connections – guided study for ninth period and lastly, Social Studies for tenth period.

On Tuesday, March 22, 2005 I followed “Gloria” around all day. When I first found out that I was supposed to follow a 13-year-old seventh grader around her school all day, I was nervous. I was worried that she would feel self-conscious and embarrassed that I was there; however, this was not the case.

1st Period – PRO-Time: “Gloria” showed up at 8:40 am for class that began at 8:45 am. She had wet hair, a cute black sweatsuit, and white Nike tennis shoes. She quietly went to her locker, got her notebook and went to class. She had quiet participation in a conversation with other classmates before class started. Some girls were talking about gymnastics – “Gloria” just listened. “Gloria” got out a sheet of fruit stickers, which the girls passed around to see what they wanted to wear. “Gloria” selected a sticker that looked like a bunch of grapes and placed it on her left cheek.

Class started with the Pledge of Allegiance and Announcements. The teacher then read off history/ social studies trivia questions. “Gloria” never raised her hand.

PRO-time was a free period where some kids were playing some sort of basketball game with garbage cans, and others sat around talking. “Gloria” sat in on a conversation with four girls who were discussing hair. The girls decided it would be fun to “change names.” “Gloria” decided to now go by “Cody” (a boy student’s name).

2nd Period – Reading: The students were given a worksheet. “Gloria” sat quietly, taking out a pen to circle the answers. “Gloria” completed the worksheet rather quickly and sat quietly, looking at her neighbor’s textbook cover and biting her pencil. Then the students were instructed to exchange their paper with a neighbor to correct. “Gloria” listened very well, while looking around the classroom. One of the kids said they had the Oscar Mayer Bologna song in their head. The teacher said, “well don’t start singing it or it will get in ours too.” After the worksheets were reviewed, and they were transitioning to a period of silent, sustained reading, the student began singing the song. The teacher used this as an opportunity for some lighthearted transitional humor. She began singing songs for very little kids, such as from The Wiggles, Barney, etc. This amused “Gloria”.

“Gloria” brought a book to read, called “Swallowing Stones,” by Joyce McDonald. During the first eight minutes of this silent reading period, “Gloria” was distracted from reading (looking up) 7 times and only turned the page once. Then she put a bookmark in her book and got a Teen People magazine from her neighbor. She only looked up three times from her reading this time (the last time – to look at the clock). After 20 minutes of reading this magazine, with two minutes left of class, everyone stopped reading, and “Gloria” used this time to stretch and chat.

3rd Period – Math: The class started with a short quiz. Then an overhead was turned on showing the class schedule:

o Content Objectives – students will learn properties of various shapes

o Language Objectives – students will take notes on shape

o Warm-up – quiz

o Homework Assignment – correct test

o Materials Needed – notebook, pencil

“Gloria” did the quiz, then got out her assignment notebook. When everyone was done with their quizzes, the students traded their quiz with a neighbor. “Gloria” got all five of her questions correct. The class was reminded that the worksheets are due at the end of the quarter (in two days).

Then the class was given a lecture on polygons. “Gloria” was attentive, and took notes. She appears to get concepts quickly, then ceases to pay attention – zoning out. “Gloria” also never raises her hand; however, when called on by the teacher, she tends to know the answer. She continued to write notes then stare off into space. “Gloria” took two pages of notes.

After the lecture, the students were instructed to work on their flip charts with a neighbor, which is also due in two days. While working with her neighbor on their flipcharts, “Gloria” explained some questions the other student seemed to have about the worksheet. She seemed very comfortable and confident with the material.

Because it took the class two minutes after the teacher first tried to get them to quiet down at the end of class, she made them stay two minutes after the bell. Although “Gloria” was sitting quietly the whole time, I was surprised that she was not upset that she was getting in trouble for other students’ misbehavior.

4th Period – Native American Connections: The class started out with a test – the students were supposed to have a pencil and sheet of paper out. At first “Gloria” only got a pencil out (wasn’t paying full attention). There was a Native American man from the Multi-cultural Center leading class (as he does every Tuesday). The instructor said that new students were not required to take the test, and “Gloria” joked, “I’m new!” The instructor laughed, and “Gloria” got paper out and prepared for the test, which was 20 questions regarding Lakota / Sioux language, history, and culture. Some of the questions were Lakota vocabulary such as directions, and he would say a word or phrase and ask what it means. “Gloria” appeared bored through much of this. The instructor’s last test question was, “Who’s a better teacher, your regular instructor, or I – – – think carefully. There IS a correct answer to this!” The class really liked this joke, and when they went through the answers to the test, many of them loved telling him the answer to the last question was either him or the regular instructor, and why. He pretended to be proud or offended as applicable.

The instructor taught the students the words / message / ‘tune’ to the Sun Dance Song. He explained a little about the ceremony, and said that he has participated in the Sun Dance before, which is one of the Lakota’s most sacred ceremonies. While they were going over this, “Gloria” was laying her head on her desk, and whined, “I don’t like that [having to sing the song].” She sat there, smirking most of the time, and not singing.

At the end of the class, The instructor said the class would be learning and playing the Moccasin game next week, which is played with four pieces of deer hide and 1 chip (kind of like ‘3-card monty’). Each team will have seven sticks. If they guess wrong (playing the game) then they have to give a stick to the other team. They are to play until one team has all the sticks. During all of this explanation, “Gloria” was leaning back in her chair, clearly bored. Since there was a little time left-over, the class did a game with multiplication flash cards – ‘Around the World’. Instantly, “Gloria” was alert and engaged, and begging to go first. The class had a great time playing this game until the bell rang.

5th Period – LUNCHTIME: When we got to the cafeteria, the children were expected to sit at assigned seats. While going to her table, a boy came up and was pushing / wrestling “Gloria” down, teasing her. It was clear that “Gloria” both liked and hated the attention. I noticed that the girls, for the most part, were all still wearing their stickers. One girl wasn’t, because she said that a teacher felt that she was being disruptive by wearing the sticker on her cheek, and made her remove it from her face. The girls were still playing the game where they were to use different names.

During lunch, the girls talked about who’s going out with whom. On the way to the next class, “Gloria” and her best friend “Melissa” walked down the hall shouting out to boys, “”Gloria” wants to go out with you!” “No, No! She’s joking. HEY! “Melissa” wants to go out with you!” “No I don’t, “Gloria” does…” etc.

6th Period – Language Arts: The kids came in and immediately started reading (without instruction). “Gloria” wrote in a notebook “Hello, my name is Cody.” The teacher noticed “Gloria” wasn’t reading, gave her a look, and she put the paper up and got out her book and started to read. For the next six minutes, her eyes wandered five times. She continued to zone, staring off into space, not really reading and playing with something hanging off of her notebook. She picked up her book like she was going to read, then began drawing on her notebook cover. The class stopped reading six minutes after they started, and it did not appear “Gloria” read at all during that time.

After the brief reading period, the teacher lead them through an assessment practice – working on revising and editing through the use of the overhead and a language arts assessment worksheet. They then finished reading a story called “Immigrant Kids” from their textbook, followed by a quiz. The class was learning about finding the main ideas in a story and drawing them out of the paragraphs. While the teacher was reading, “Gloria” read along. Then the class was expected to write in their notebooks the main idea and three supporting details. “Gloria” wrote like this:

MAIN IDEA

a. Immigrants had to help officers…

b. Before immigrants….

c. When the immigrants…

The teacher’s instructions were suggestive that the students should write something more like:

IMMIGRANTS ARRIVE AT ELLIS ISLAND

a. Had to be examined

b. Had to answer a series of questions

c. Had to ….

She worked quietly on the next Main Idea assignment, and then had a quiz to complete. Once she was done with the quiz, she was supposed to have free reading (choice reading) – if time allowed. “Gloria” finished the quiz and went on to the word search on the back of the quiz.

7th Period – Science: This class was all about preparing for the end of the quarter by getting an assignment turned in to be graded by Thursday. The students were working on their science logs.

I noticed a trend among the teachers throughout the school day during this visit – they continued to remind the students of two things:

1. The third quarter ends in two days

2. Since “we’ve been talking about / doing x-y-z for 3 quarters now…” “There’s only 9 more weeks of school…” “You need to start thinking like 8th graders, since you’re practically there…”

“Gloria” sat, waiting patiently to have her science log stapled by the teacher, who came around to each student individually, to do this himself.

I found that “Gloria” does very well with:

o Following instructions

o Doing assignments with ease (quickly)

o Not disruptive in class – doesn’t join in when others are disruptive

The students were instructed to give their logs to a neighbor, and put point values for certain types of information present on each page (basics such as page number, title, # of items expected on page, etc. – – – not for content). The student would get a 1 if it was all there, and a zero if it wasn’t. When “Gloria” was done looking at the other student’s science log, she sat quietly, nibbling on her nails. When “Gloria” got her science log back from her neighbor, the teacher walked by and glanced down at her paper (where the points were assessed), and said, “Good job!” “Gloria” smiled quietly to herself.

8th Period – Keyboarding: This was BY FAR the hardest class for which to shadow a student. The students work independently – there was next to no interaction with each other or the instructor (which was a substitute today). “Gloria” first worked on a Words per Minute (WPM) timed test, and was required to record her results on a log. Then she did spelling and punctuation tests, and worked on skill builders. There were a lot of options available for skill building, such as various word/ mouse games, but “Gloria” chose straight keying practice lessons (for speed/ accuracy).

9th Period – Native American Connections – Guided Study: This is the class that I normally observe on Thursdays. During this day, I noticed that “Gloria” had photos on the cover of her notebook. I asked who they are pictures of, and she said they are two cousins and three friends. One of the friends is a boy over whose picture she has written the word “hottie”. “Gloria” put three more pictures on the back of her notebook (using teacher’s scissors and tape), which was not exactly studying; however, the teacher did not take notice of this.

“Gloria” used this class period to complete the flip chart from math class. She was actually pretty focused for study hall. This was the quietest I have ever seen this room. Everyone appeared to be on task today. Of course, the louder students were not in the room today. Two boys and two girls were sent to go work on their language arts research papers with their teacher and/or go to the library to avoid getting an F for the quarter in that class.

I noticed that “Gloria” has one of those “hope” pink rubber bracelets on her left wrist. She has written the name of her best friend “Melissa” on it. On her right wrist, “Gloria” has a blue hair scrunchy, although she has not had it in her hair all day. Near the end of the class, the math project was complete, so “Gloria” spent the rest of the time taping pictures to her notebook. I find that observing an “at risk” student in study hall is a good setting because they are off-task so much; however, this was not the case for anyone on this day (at least not in this class). The instructor looked at “Gloria’s” math flip chart when she was done and told her, “This looks really nice, ‘Gloria!’ “

10th Period – Social Studies: There was a student teacher, for this class. He put the following objectives up on the overhead for the day:

– Daily Focus

– Section 4 assessment

– Chapter 17

– Geo test today (Asia test tomorrow)

“Gloria” had focus issues in this class, and was writing on the desk behind her. She was supposed to be writing a hypothesis regarding “The Bedouin Tent” – from overhead slides reflecting tent terminology (i.e. mog’ad – or sitting place for men entertaining guests; ma’had – woven curtain between men’s/ women’s sitting place; maharama – place for women). The teacher tried to engage the students in a discussion regarding this material (i.e. “why do you think the mag’ad is used by only men and guests?”). The class was less than enthusiastic with the material. “Gloria” was staring off again, not writing answers, writing down the ideas people came up with and talking to her neighbor.

Apparently, yesterday they did group projects on page 496 of their Geography books and now were required to write in their journals regarding what they learned. The teacher instructed the students to pair off and work together. Left to their own devices, the students did not get into pairs right away, wasting a lot of time. A couple of people paired up, but most of the class worked on the task individually. “Gloria” chose to work on her own, answering questions to the chapter. All sorts of disruptions were going on in the room, but “Gloria” stayed on task. During class discussions and assessment, “Gloria” never raised her hand, and stared off while chewing on her pencil.

The students were given a Geography test covering weeks #21 through #24. The teacher told them they could prepare/ study while he sets up the quiz. “Gloria” was writing on the desk (cheating? – – -I never looked to confirm). “Gloria” completed the quiz and put her journal on the back table.

Over the weeks, I have observed that “Gloria” is typical for a girl her age, according to NMSA (2003), in the following ways:

Physical Development –

o Often restless and tired (everything is ‘boring’)

o Increased sexual awareness (as evidenced in her spoken and written comments about boys being “hotties” and previous observations of her assignment notebook, etc.)

Cognitive – Intellectual Development –

o Prefers passive learning (observing rather than volunteering to give answers)

o Prefers to work independently when given a choice of working alone or in pairs

o Challenges rules / authority (gum-chewing a big issue for “Gloria”)

Moral Development –

o Has problem with “cultural acceptance” according to her instructors – feels is superior to other ‘more Native’ students

Psychological Development –

o Self-absorbed

o Aware of ethnic identity, but struggles with accepting it in herself / others

o Likes recognition for accomplishments – even a simple ‘thank you’ or ‘good work’ are important to her

o Has a positive outlook

Social – Emotional Development –

o Strong need for approval

o Strong need for peer acceptance

In speaking with “Gloria’s” instructors, I learned some more interesting insights into what makes this child “tick.” According to her Native American Connections instructor, “Gloria” is extremely bright. She is more motivated socially than academically. She is struggling with her identity and is a bully. She picks on other students who are more “Native” than her. She talks about them, threatens to beat them up. She is struggling with her Native American identity. By targeting the “more Native” students, she is attempting to define her place in the pecking order. In comparison to these other Native American students, her family is more affluent (more financially well to do). “Gloria” also struggles with the Lakota value system – she fails to take it seriously. She is more assimilated with white / dominant culture and torn / turns away from Lakota culture.

The instructor and I have both observed that “Gloria” likes to break minor rules (i.e. gum-chewing…she did this several times throughout the day – a teacher would call her on it and ask her to spit it out. “Gloria” did this reluctantly, but then in the next class she’d have gum again. Part of this was achieved by “pretending” to throw the gum away, and partly getting the gum from somewhere. I have no idea when and/or where the gum ever came out and was put in her mouth. It just materialized.

The Native American Connections instructor believes that “Gloria” will graduate from High School. Math engages her. She focuses and gets right to it. “Gloria’s” Grandmother lives with her and she believes in the importance of education. “Gloria’s” mother is less focused on education for her daughter; therefore, the child is torn as to what is best, because she doesn’t want to hurt either important authority figure in her life. When I asked what the instructor thinks “Gloria” needs most, she said discipline for unacceptable behavior (inappropriate notes, bullying, etc.) for which she has received In-school suspension (ISS), Staying After School (SAS – detention), etc. as a result.

I then spoke with the PRO-time instructor, who felt “Gloria” is very quiet, shows independence – blatant disregard for rules (i.e. gum-chewing) – which is a control issue for “Gloria”. She wants someone to tell her she has to spit the gum out. The PRO-time instructor said that “Gloria” definitely works below her potential. She is missing some basic skills. This instructor said that “Gloria” is good in class, is very organized (and detailed in her planner) but will be left behind because she’s quiet. “Gloria’s” Mom missed her 1st quarter conference (called and said couldn’t make it). Her Mom came to the 2nd quarter conference and was asked by the PRO-time instructor to allow her daughter to be put in an 11th period. This is an opportunity for students to catch up on work, since they may not have time at home; plus they can get assistance with assignments with which they are struggling (like additional guided study time).

I would recommend the following for “Gloria” – increased use of games as a learning tool – according to Wormeli (2001, p.49) games are “intrinsically motivating…When people have fun, they don’t realize they are learning.” I completely agree. During my day of observation, all of “Gloria’s” classes had the students engaged in seatwork, quizzes, and reading / lecture activities. “Gloria” seemed to really respond to the game that took place in the Native American Connections class – and that was clearly an opportunity for kids to show their knowledge of subject matter – multiplication and division flash cards.

I did not observe any “true” collaboration in any of the classes, other than kids working together on their own individual projects in math, and being given the option to pair up in Social Studies. I would like to have seen the student teacher actually pair the students up himself, so the children didn’t feel they had a choice. As I indicated above, when left to their own devices, the students did not pair up; however, there is definite benefit to such activities, and I would like to see “Gloria” learn how to participate in such.

I would like to see more integration of coursework between classes – I saw no evidence of such activity; however, I did observe it on one of the Thursdays when I came to observe. The kids were working closely with some Native American individuals from Wisconsin who were teaching them to make model “Tipistolas” (tipis). Apparently the activity integrated concepts from (and was worked on during) math class, art class and Native American Connections. Later in the semester, I also observed children working on ‘bead looms’ in the Native American Connections classroom; however, I never learned if this was coordinated with any other class such as art or even math (patterns).

I noticed that “Gloria” never voluntarily speaks up in class; but when called on, is attentive and usually has the correct answer. This is touched on in Wormeli (2001); however, I found an interesting article regarding learning styles of Native American adolescents which also talks about this subject matter (More, 1989). In this article, Mr. More indicates that Native American culture focuses on a more “think-then-do” approach to learning rather than the traditional classroom’s “trial-and-error” approach. Native American students would rather think about the question and make sure they have the correct answer before just “blurting out” the answer and getting it wrong.

I would like to see more of her teachers providing differentiated instruction, to reach children’s differing intelligences. I realize that the day I observed was so close to the end of a quarter, that there was a lot of “house-keeping” being done. This may explain the ‘boring’ instructional techniques. According to another article that I read regarding teaching styles for Native American students (Swisher & Deyhle, 1989), Native American students “tend to approach their world visually and by quiet, persistent exploration…a style of teaching stressing overt verbal performance is alien to such a child.” So lectures are not always the best way to go with these students, at least not all the time.

I don’t completely agree with this perspective as it relates to “Gloria” because she showed a great deal of competence in taking notes, and was content with quiet activities. I would just like to see things “shaken up a bit” in these classrooms, to engage the students in their off-task behaviors. For example, during the Social Studies lesson, I believe that the students would have better responded to a game of jeopardy regarding the tents of Bedoins rather than a worksheet / review. I understand that the teachers needed to assess the students for quarter-end, and that grading a piece of paper is easiest; however, Middle School students need variety and creativity from their teachers and their lessons. Most of the teachers only were instructing to the “verbal / linguistic” intelligence of their students. Maybe a game like the one presented in the Native American Connections class, where the kids stood and when they got a question right, they got up and didn’t have to sit again until someone else got one right. Then that person had to sit in the first person’s seat, etc. It was fun, kids had to “think on their feet” and they got to move around a bit. Plus it let them reinforce material they had already learned.

According to an article I read in the Middle School Journal (McCabe & Greenwood, 2005), “People tend to avoid tasks and situations they believe exceed their capabilities, but they undertake and perform assuredly activities they judge themselves capable of handling.” This appears to be true for “Gloria.” When I asked her what her favorite subject is, she said Math, with no hesitation. It is evident that math comes easily for her, and that she enjoys it. In fact, I think it might not be a bad idea to try to give her a chance to perform more challenging math work.

I found that “Gloria” might not enjoy reading. Although I never asked her why this is, it is possible that she does not feel it is something she does well. This negative self-efficacy toward reading is evident in the amount of off-task behavior exhibited during periods of quiet reading time. Perhaps instead of just giving students 10 – 20 minutes of sustained reading, I would like to see more accountability for that reading. Keep a journal about what they are reading, how much they have read, what occurred during the reading, etc. With specific direction as to the application of that reading, “Gloria” may find it easier to stay on task. During her Reading class, I’m pretty sure “Gloria” couldn’t tell you what was happening in her library book, but she probably knew everything from who’s dating whom to what Hillary Duff or Lindsay Lohan wore to recent red-carpet events (from the Teen People magazine).

With regard to “Gloria’s” acceptance of her cultural identity, I think the school is doing the right thing, having the students involved in learning about traditional Lakota culture, via Native American Connections classes. The things about bullying and self-created “class distinctions” are no different than any other ‘bullying’ type of behavior. The school has a strict bullying policy, which apparently she has been held accountable to in the past (ISS, SAS). I would encourage something along the lines of a behavior analysis which can be a helpful tool to focus students on acting responsibly and learn accountability (Wormeli, 2001, p. 202). When incidents occur, this form requires the student to:

o Describe the behavior / incident in their own words

o Talk about their feelings about the incident (and look at how others involved might have felt)

o Indicate what the student will do to prevent similar incidents from occurring

o List what they plan to do to re-build trust (with the other student, teacher, school, etc.)

I found that the school is filled with positive messages reminding students of the six pillars of good character (Character Counts), as well as other positive messages. I noticed that the Reading classroom had a poster regarding RESPECT, which said:

Realizing

Every

Single

Person

Expects

Consideration of

Their feelings

I really liked this message, and think that it is an easy way for kids to remember to respect each other and their feelings. I believe it should be changed to say “Their feelings and individuality”.

I learned a lot through this experience, and feel that overall “Gloria” is a good kid, with a good head on her shoulders. Hopefully, she will discover a way to balance her need to be social with her need to get a good education. She requires good, positive adult role models in her life, such as her family (mother, Grandmother, sister) as well as her instructors at this school, which I think do a great job of keeping her grounded and focused as best they can. I liked the way the instructors worked together as a team, sending each other e-mails keeping on top of what each student is doing, what they are lacking, etc. In that way, the students are treated as individuals, and shown individual respect, which is very important at this age.

REFERENCES:

Jerkins, R. (2001). Not a Girl, Not Yet a Woman [recorded by Spears, B.] Britney. Zomba Recording Corporation. Lyrics retrieved 05/09/05, from http://www.lyricsdownload.com

McCabe, P. & Greenwood, S. (2005). Using learning contracts to enhance students’ self-efficacy for reading and writing. Middle School Journal. 36(4) 13-19. Ohio: NMSA.

More, A. (1989). Native Indian learning styles: A review for researchers and teachers. Journal of American Indian Education – Arizona State University. Retrieved 04/16/05, from http://jaie.asu.edu

National Middle School Assoc. (2003). This We Believe. Ohio: NMSA.

Swisher, K. & Deyhle, Donna (1989). The styles of learning are different, but the teaching is just the same: Suggestions for teachers of American Indian youth. Journal of American Indian Education – Arizona State University. Retrieved 04/16/05, from http://jaie.asu.edu

Wormeli, R. (2001). Meet me in the middle. Maine: Stenhouse Publishers.

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