Statistical Process – Voice Over Power Point

Dr. Higgins,

Thank you so much for posting that PowerPoint, it really helped!  I had the PowerPoint playing on one side of my screen and typed out some additional notes on a blank Word document I had opened on the other side of my computer screen.  I found the text alone really informative, but I also appreciate you adding the voice over as well.  I find that information sticks better with me when I hear it.  There were a few things that you said in the PowerPoint that weren’t necessarily typed on the slides that I took note of.  For example, I liked your idea of supplying different colored pastas to students to help them categorize into different groups.  As you can read in my earlier posts, I had my reservations about using kids’ shoes or having them count how many pockets they’re wearing because I was scared that it would emphasis material possessions and focus on the students’ outfits and the social misconceptions that go with them.  Although I realized that it’s all in the way the instructor presents and teaches the lesson, I still really like the idea of using pasta.  It’s cost effective and it’s still fun for the kids. 

            You also mentioned simple hints such as supplying students with a list of their classmates’ names when they’re collecting data.   Students can scratch off each other’s names as they collect data from one another, making sure to record only one answer for each student and to receive an answer from everybody.  It’s those little helpful hints like that, that I think come in handy to note when you’re a new teacher!

            I thought the story about the student who placed a square and hexagon together to make a flower was cute, but also served an important moral that teachers need to be careful with their choice of words and to be sure to teach students the proper mathematical vocabulary.  In my earlier post about the How Many Pockets video, I wrote about how I appreciated how the instructor took the time to correct a student who mistakenly said, “Most of the people have 5 pockets” instead of “A lot of the people have 5 pockets”.  While some mistakes may seem small, I think it’s important to correct to ensure that the student is made aware exactly of what is being asked of them and what they’re answering back.  As a student, you have to understand both in order to be truly learning the concepts at hand.

            I took a look at the website: http://nlvm.usu.edu/en/nav/frames_asid_270_g_2_t_3.html?open=instructions and even played around a bit on it.  When you hit “Check” it automatically knocks the wrong answers out of the circle, which I thought was resourceful.  I wish it had a button that students could push that explained Why though.  For example, a message could pop up and say “that triangle is blue, not yellow like every other block inside the circle”.  Although I think it’s a great online math manipulative, I think it would be beneficial because I’ve seen so many students use the check button almost as a cheat button as they mindlessly work on these online applications during independent computer time.  I know they say that the instructor should always be aware of what the students are doing when they’re on the computer, but I just don’t think it’s realistic to assume that the instructor is going to be watching over they’re every move.  A quick “WHY?” button would help to make this website an even greater online tool for students to use independently.   

 

 

How Many Pockets – Video Introduction

Last semester I completed my field experience in a second grade classroom and I remember going over how to properly build and write lesson plans with the teacher.  She told me that when you teach anything, first you want to demonstrate it, than you want to guide the students to do it, and then finally you let the students do it themselves.  You move from demonstration, to guided practice, to independent practice.  Watching this video made me think about that, and I was pleased to notice that the instructor in the video used the same method.  Before she even asked the students to count their own pockets, she defined what a pocket was and showed the class how many pockets she had.  At one point in the video, there was a student who wasn’t able to count how many pockets she had, so she let her classmates help her to discover the answer.  Instead of helping the student out one on one and taking her attention away from the whole class, I really liked how the teacher used the student has a demonstration for the entire class- reinforcing the concept of how to collect the data.  As she stood in front of the class, everyone counted how many pockets she was wearing together.  So at first she demonstrated on herself by defining and showing the class how many pockets she had, then she used another student as an example of guided practice with the whole class, and finally she had the students count their own pockets independently.

I also liked how the instructor pointed out what might be considered unusual data- the student who only had one pocket.  Instead of just graphing the data and moving on, she took the time to go over with the class why this particular data might be surprising to some.  For instance, she had the student point out that his one pocket was from his t-shirt, not his pants, which was unusual compared to the other students’ data.  As a class, they also interpreted the data to state that nobody has 3 or 10 pockets.  When we analyzed our data on who we would like to have a conversation with, one of the questions you asked us was if there was any data that didn’t fit into any of the categories and what we did with it.  I think it’s important when learning about data analysis that you always look for the “unusual data” and understand why it’s unusual.

I’m not going to say that it “struck me”, but something that I was reminded of when it came to the students’ thought process in the video was that you really have to use baby steps when teaching.  For instance, it would be so easy as a teacher just to say 2+2 is 4 and have all of the students agree.  But unless you take baby steps and explain and TEACH the students WHY 2+2 = 4, then you’ll find a completely lost class when you ask them what 3+3 is.  There are times in the video that you see the instructor call on students who aren’t paying attention or will ask someone to just repeat what a previous student already said, and it takes a couple of kids being called on in order to do so.  This is all so typical!  Nothing about teaching is perfect, and I think these moments made the video much more realistic to what really happens in the “real world classroom”.

When I refer to taking baby steps, I mean that the instructor started with a general question at first – “What do you notice about the data?”.  One of the students answered that 5 had the most marks.  The instructor then asked the class to expand on that thought – and eventually another student interpreted the data to state that “A lot of people have 5 pockets”.  So the instructor took baby steps and 1) started with a general question, 2) called on one student to answer, and then 3) had that student’s classmates expand on that original thought.  I really liked how she encouraged the students to help each other out, incorporating peer-to-peer learning.  I also appreciated that she wrote “A lot of people have 5 pockets” on the board so students not only verbally heard the answer, but saw it as well… and if she left it on the board, then it’s something they could see and reflect about later on as well.  From there, she even further expanded the original statement of “A lot of people have 5 pockets” by asking the students “WHY?”.  This leads to the 4th baby step- pushing the students to a higher learning, or critical thinking…Why would we might predict and expect a lot of people to have 5 pockets?  Which eventually lead the students to realize that most jeans have five pockets, and a lot of the students were wearing jeans.  There was also a point where one student mistakenly said “Most of the people have 5 pockets”, and the instructor pointed out the difference between “most people” and “a lot of people”.  If it’s anything that struck me about the teacher’s moves, it was a combination of these small but very effective things she said and incorporated into her teaching style.  I’m sure she didn’t write “go over the difference between most and a lot” in her lesson plan, but it’s these spontaneous moments that you so often have in the classroom that really justifies how capable you are as a teacher.

Throughout the video, I thought the teacher did a great job keeping the class on task (which isn’t so easy with young kids).  Each move or action, and everything she said, had a purpose.  From little class management techniques such as “when you’re ready, give me a thumbs up” to keep the class quiet and focused, to explaining to the whole class why she’s changing the data when certain students wanted to change their answer to how many pockets they have- it was all done with a purpose.  I especially liked how she talked her thought process out while changing the data, saying things such as I’m erasing one x from the seven and adding one x to the eight because you first told me you had seven and I marked it down, but now you found one more pocket, so I’ll mark you down for having eight pockets.  One of my biggest issues I’ve found (from my little teaching experience so far) is that I have a hard time staying within the time frame I’ve designated for each lesson.  I’m always scared I’ll run out of time so I tend to rush through certain parts that I later wished I had taken more time with when I reflect upon how the lesson went afterwards.  There are little things that the instructor in this video did that I hope to incorporate into my lesson plans.  And several of the things she did didn’t take up that much additional time to the lesson at all.  For instance, just giving the students a few more seconds to think over their answers before calling on anyone, or asking the class what the next point on the line plot is when first collecting the data instead of just writing it all out (i.e. First we counted how many students had zero pockets, than we counted how many students had one pocket, what should we count next?).

There were a lot of different ideas that the students were working on: how to collect, record, interpret and analyze data.  In doing so, I heard the instructor use key vocabulary words such as line plot, point, range, etc.  And as I mentioned before, I think one of the most important things the students were working on (whether they knew it or not) was expanding on one another’s ideas and thoughts to critically understand the lesson being taught.  For example, one student noticed that there were ties among the data, another student pointed out one of the ties (that 1, 4, 7, and 8 all had 2 x’s), and a third student interpreted that tie to mean that 2 people have 1 pocket, 2 people have 4 pockets, 2 people have 7 pockets, and 2 people have 8 pockets.

Overall I thought this classroom activity was comparable to The Shoe Problem from our Teaching Children Mathematics article.  I know these classroom activities provide a great lesson for teaching students about data collection and interpretation, but I think you also have to be careful doing them when you’re dealing with students’ clothes.  You don’t want to individualize a student who may be wearing something different from all of their classmates and ends up being embarrassed by it.  So at first, I thought that I wouldn’t want to do these types of activities, but after reading the article and watching this video, I realized that it’s all in the way that you as an instructor handles it.  For instance, in the video, the instructor uses one of the students (the girl with 11 pockets) as an example in front of the whole class, but the way she handled it made the students focus on the lesson being taught instead of thinking “why’s she different?”.  And making the data personally about the students in the class, I think helps to keep their attention on the lesson and shows them how math could be directly used in their lives.

 

 

 

 

Statistics as Problem Solving

Wow!  This site is pretty amazing!  There was so much information and I enjoyed the video segments that were incorporated as well.  I also appreciated how the correct solutions were available to look at too.  There’s so many other websites out there that have great questions, but I’m always hesitant that my solutions are wrong.  I liked how it didn’t just say when answers would vary either, but it explained why the answers would vary and gave an example of a correct answer. 

Here’s a few of the notes that I copied to help me study for the midterm:

(http://www.learner.org/courses/learningmath/data/session1/index.html)

  • Statistics is a problem-solving process that seeks answers to questions through data.  This process typically has four components:

1) Ask a Question

2) Collect Appropriate Data

3) Analyze the Data

4) Interpret the Results

 

  • Data consist of measurements of a particular variable. Data are defined in terms of variables, or characteristics that may be different from one observation to the next. When we measure these characteristics, we assign a value for each variable. This set of values for a given variable is known as data.
  • There are two types of variables — quantitative and qualitative.
  • Variation, or differences in measured data, occurs for a number of reasons. Examining variation is a crucial part of data analysis and interpretation. In fact, explaining the variation in your data is as important as measuring the data itself.
  • There are many sources of variation in data, including random error and bias.
  • Random error is a nonsystematic measurement error that is beyond our control, though its effects average out over a set of measurements. Over repeated uses, however, the effects of these random errors average out to zero. The errors are random rather than biased: They neither understate nor overstate the actual measurement.
  • Measurement bias, or systematic error, favors a particular result. A measurement process is biased if it systematically overstates or understates the true value of the measurement. If a scale is not properly calibrated, it might consistently understate weight. In this case, the measuring device — the scale — produces the bias. Human observation can also produce bias. The important thing to keep in mind is that biased measurements invariably produce unreliable results.
  • Bias in Sampling – The entire group that we want information about is called the population. We can gain information about this group by examining a portion of the population, called a sample. To gain useful information, the sample must be representative of the population. A representative sample is one in which the relevant characteristics of the sample members are generally the same as the characteristics of the population. How we select a sample is extremely important. Improper or biased sample selection can produce misleading conclusions. Sample selection is biased if it systematically favors certain outcomes.

Teaching Children Mathematics

Franklin, C. A., & Mewborn, D. S. (2008). Statistics in the elementary grades: Exploring distributions of data. Teaching Children Mathematics, 15(1), 10-16.

 

Here are my notes from the article:

 

“School teachers have long engaged elementary students in collecting and analyzing data but have often neglected to involve students in formulating the questions to be answered (so that the data are relevant and meaningful to students) and to provide opportunities for students to interpret data they have collected in light of their original question” (10).

 

The Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report

1. Formulate a question that can be addressed with data.

2. Collect data to address the question.

3. Analyze the data.

4. Interpret the results.

 

Exp. of Categorical Data – The Shoe Problem

  • “What is the most popular type of shoe in our class today?” can be linked to other questions that are relevant to the students’ lives such as “How many students are prepared to go to physical education class without changing shoes?”
  • Critical idea is that whatever classification is used, the resulting data will vary bc not all students will be wearing the same type of shoes.
  • Use various representations (graphical and numerical) for summarizing data distribution- as it is one of the most important concepts in statistics.
  • Elementary teachers often neglect to guide students to look beyond the “pictures” the students have created…. Do all categories contain about the same number of shoes?  Do some contain more shoes or fewer shoes than others?  Can you locate yourself in the representation?  What if we collected this data in a school in Hawaii?… get students to note reasons for differences in distributions of data (the WHY? question!)

 

Exp. of Numerical Data – The Soccer Problem

  • Level A statistical questions involving numerical data allow students to develop an interpretation of the mean and begin to explore quantifying variability in the data… the number of goals scored by soccer teams on a particular weekend?
  • Involve students in what data to collect and why.
  • Ask students what they know about the data, and generally they’ll group them from lowest to biggest.  Just as in the shoe problem, students should note that the scores are not all the same.  The scores vary from one game to another.
  • The fair, or equal, share value for the data – Based on all the goals scored from these nine games, what would be the game score if all games resulted in the same score?  Answer: The fair share value for these data is 4 and 7/9.  The closest we can come to having a fair share value is for seven of the games to have a score of 5 and the two remaining games to have a score of 4.  Eventually, students learn that the fair share value and the mean represent the same quantity for a collection of data.
  • Would we expect the score from every game to be exactly the same next weekend?  Why, or why not?  Focus students to think on the issue of difference in distributions of data and what contributes to variation in the data distributions.  These questions may not have clear cut answers, but the objective is not to find the answer but for the students to pose various factors that could influence the data.
  • Extend the activity by reversing the process for determining the fair share value.  What if none of the games had a score of 6?

 

 

What if questions help students begin to understand the nature of variability, a fundamentally important concept in data analysis” (16).

Categorical Data Sort and Analysis

    When I first looked over the different names, I was surprised that I didn’t recognize all of them.  For example, I had no idea who Lev Vygotsky, Haregewoin Teferra, or John Melia were until I read Rachael’s, Dr. Higgins, and Brittany’s blogs.  I also noticed that there were a lot of repeats as well, which I guess I kind of expected.  I once heard that when asked if you could meet anyone, that Jesus Christ was the #1 answer of any random group of Americans.  So I thought it was interesting that it was our most repeated answer, but I wasn’t surprised. 

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    I attached pictures of how I ended up sorting the data, but here’s what I came up with (just in case the pictures aren’t clear enough):

 

Figure from the Past – Died more than 100 years ago

Jesus Christ (3 times)

Thomas Jefferson

George Washington

Helen Keller

The Wright Brothers

 

Figure from the Past – Died in the past 100 years

Princess Diana (2 times)

Lev Vygotsky

Martin Luther King Jr.

Fred Rogers

Marilyn Monroe

Margaret Mitchell

Ghandi

Hank Williams Sr.

Earnest Hemingway

Haregewoin Teferra

Dr. Seuss

 

Modern-Day Figure

Maya Angelou (2 times)

Peyton Manning

Warren Buffett

Tina Fey

Judy Bloom

Ron Clark

Pope Francis

John Melia

Michelle Obama

 

    As you can see above, I split the data into three different groups: 1) Figures from the Past, People who died more than 100 years ago, 2) Figures from the Past, People who died in the past 100 years, and 3) Modern-Day Figures.  When I was trying to decide how to group the data into different categories, I realized that we all chose our role models, or people that we look up to and admire what they offered the world (whether past or present).  For example, no one said they wanted to have a conversation with Hitler to ask him why he did what he did.  I thought it was interesting to see the different role models that we all had in the class.  As aspiring teachers, we’ll all be our students’ role models one day as well, so it’s interesting to see who we look up to.  The reason why I chose to categorize the names by their different lifetimes is because I always hear on the news and from various people that the youth growing up these days don’t have role models like they used to in the “good old days”.  For instance, just take a look at the celebrities in Hollywood now.  Kids are looking up to people like Chris Brown and Lindsay Lohan, just because they’re celebrities and rich. 

 

    From our class, 7 people chose role models who died more than 100 years ago, 12 people chose role models who died in the past 100 years, and 10 people chose role models who are still living.  I would say the data is pretty evenly distributed among the three different groups.  So it was refreshing to see that there are people still living today who make great role models, such as Pope Francis, Maya Angelou, and Ron Clark.  But I guess you could also interpret the data differently and say that 19 people chose role models who are deceased, while only 10 chose role models who are still presently alive.  If you look it at that way, than the thought that there are less role models in this world than in past generations could be argued to be true.  19 to 10- that shows almost twice as many role models from the past than in the present. 

    Based on this initial data, a question that I would want to pursue would be the ever important one of WHY?  Why are these people thought of as role models?  Which leads to the second way that I chose to organize the data.  Although I know we weren’t required to post the second way we organized the data, here’s what I came up with: 

 

Religious Figures

Pope Francis

Martin Luther King Jr.

Ghandi

Jesus Christ (3 times)

 

“Hollywood” Celebrities

Tina Fey

Marilyn Monroe

Hank Williams Sr.

 

Authors

Judy Bloom

Maya Angelou (2 times)

Margaret Mitchell

Earnest Hemingway

 

Advocate for Children/ Education

Ron Clark

Fred Rogers

Haregewoin Teferra

Dr. Seuss

 

Government Official/ Royalty

Michelle Obama

Princess Diana (2 times)

George Washington

Thomas Jefferson

 

 

Lev Vygotsky – Psychologist

Helen Keller – Activist for people with disabilities

John Melia – Supporter for American troops

Peyton Manning – Athletic figure

Warren Buffett – Business related figure

The Wright Brothers – Inventors

 

Here’s the totals, of how many of us chose people that belong to each group:

Religious Figures = 6

“Hollywood” Celebrities = 3

Authors = 5

Advocate for Children/ Education = 4

Government Official/ Royalty = 5

Other = 6

 

    If we were judging from this data alone, we might say that we as a class hold religious figures to be more valuable than Hollywood celebrities (6 to 3).  But there are a couple of things “wrong” with this data.  For instance, there are several people that could fit into two different categories.  I put Tina Fey into the category of being a “Hollywood” celebrity, but one could argue that it was her credit as a female comedic writer and author in a male driven field that makes her a role model.  I guess the only way to truly organize the data would be for me to modify the survey and outright ask people “Who is your role model that you would like to have a conversation with, and why?”.  Another problem with this data is that there’s too many names in the “other” category, in my opinion.  If you’re trying to organize a data set of 29, I think having 6 (or 21%) of the data in an “other” category seems like you should find another way to organize the data.  Leaving 21% of the data in an “other” category is almost like you’re just ignoring it, and I’m sure everyone would agree that ignoring 21% of the data is probably not such a good idea.      

 

 

 

 

 

 

 

        

 

 

 

 

 

Calvin & Hobbes

Calvin & Hobbes

I saw that Dr. Higgins had posted a Calvin & Hobbes comic strip on her own blog, and it inspired me to do the same! To this day, Calvin & Hobbes and Peanuts are still tied as my favorite comic strips. Cheers to Bill Watterson, wherever he is!

Won’t you be my neighbor?

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If I could have a conversation with anyone, I would choose Fred Rogers from Mister Rogers’ Neighborhood.  I loved his show when I was growing up!  The way he would flip his shoe was so amazing to me as a child.  I’d always hold my breath and act surprised when he caught it, haha!  Anyways, I picked him because as an adult I’ve become obsessed with reading biographies and finding out more about the people that I was fascinated with as a child- Fred Rogers being one of them.  I think the work he put towards children’s programming and education through television (probably the biggest form of mass media of his time) is really remarkable.  And now, as an aspiring teacher, I think it would be great to get his thoughts about childhood development and education.  Off to the side, I would probably ask him if any of the rumors about him being a military sniper or always wearing those sweaters to cover up his full-sleeve tattoos were true or not.  I wouldn’t be able to contain myself!  But whatever we ended up talking about, I’m sure it would probably be one of the most kind and soft-spoken conversations I’d ever have.

 

Here’s a quote from his book Life’s Journeys According to Mister Rogers: Things to Remember Along the Way.  I thought this one was a good one to share with students:

 

When we study how our ancestors dealt with challenges,

we can (hopefully) learn from their successes and failures.

 

Someone once asked Edison if he was disappointed after trying 382 ways

of making a lightbulb.  He answered that he wasn’t.

He was glad that he now knew 382 ways not to try.