Pre powerpoint information

The area I decided to focus my inquiry on is: math

This is important to me because: I have seen math overlooked at schools that are in Program Improvement.  Most schools and districts seem to be focusing a lot of energy on language arts, specifically reading.  However, students who only understand algorithms for math, but not the why and when to use them fall quickly behind.

The question I am asking is: How can students' understanding of how math is used in daily life situations help facilitate their math learning in the classroom?

The context I teach in is: I am currently not in an elementary classroom. I am, however, working in a university level classroom.  

The data I collected to answer my question: So far, I have interviewed 50 fourth grade students about their thoughts related to math and everyday uses.  I have also asked their teachers the same questions I asked them.  Within the next week, I will be returning to those same 2 classrooms (one in San Lorenzo USD and the other in Dixie SD in Marin) to have students write letters that demonstrate their mathematical thinking.  They will be given the following prompt:

Frankie is a 2nd grader in Ms. Tully's class.  He insists that 1 1/4 is larger than 1 1/3.  Ms. Tully is frustrated because he is certain he is correct.  She has asked you to help him understand his misconception or mistake.  Write a letter to Frankie explaining why 1 1/4 < 1 1/3, or write a letter to Ms. Tully explaining why 1 1/4 > 1 1/3.  You may use words, pictures, and symbols to help Frankie or Ms. Tully understand.  (Don't be worried about spelling or writing conventions.)

Also, Frankie thinks he'll never use fractions and learning about them is a waste of time.  In your letter, explain some real life examples that will help Frankie understand how and why fractions are used, or can help Ms. Tully explain this to him.

The changes I have made in my teaching practice as a result of my inquiry are: (The changes I hope to make in my teaching practice are:)  When I return to the classroom, I am planning on adding a discussion about how and why particular math skills are used in every day life as a part of my math routine.  Right now, I begin each unit with a pre-assessment and a math talk.  It is at this juncture that I plan on adding a class discussion about how they might use a particular skill or/and how they've seen adults use a skill.  
When I was at CABE last week, presenting a workshop on fractions, I discussed this with the participants and provided a chart for them (they are all teachers) to indicate how they use fractions in their daily lives. 

The changes I have seen in my focal students as a result of my inquiry are: This is a question I need to pose to the 2 teachers, as well as if they have changed their teaching and incorporated more talk about real uses of math into their instruction!

Class 2 - Looking at the data

Info: Class = 28 students, 26 were questioned

Dixie School, Marin County

4.2% free or reduced lunch

7% ELL

5.9% RFEP

Question 1: What is math?

*      21/26 answered come form of computation: +, -, x, /

*      2/26 included counting

*      2/26 included solving problems

*      2/26 said something about $

*      Unusual answers:

o   “I don’t know how to describe it, I just go with it.”

o   “applies to life”

o   “a hard subject in school”

o   “The new math program (Every Day Math) is fun, but sometimes I feel like ‘ugh’, it’s math.”

Question 2a: How do you use math at school?

*      ½ of the students indicated some sort of computation in their answer

*      7/26 made a reference to math program either by name, “math book”, “work sheets” or “tests”

*      10/26 used the word “problem” in their response, mostly indicated doing math problems or word problems

*      Unusual answers:

o   “We use it to know how much water you need to water the plants.” (I later observed a student watering the plants with a measuring cup.)

o   “In music – to count rests and beats.”

o   “At recess, like when we play basketball, we use math to count and make sure our teams are even.”

Question 2b: How do you use math away from school?

*      12/26 students indicated some use of money, paying for things, shopping

*      2/26 stated that they use it for computer games or programming (one of these students actually creates his own games)

*      9/26 stated homework as a way they use math away from school and 3 of those students also indicated that they get parental support either in the form of homework assistance or “quizzes” from parents

*      8/26 students indicated some kind of measurement  - measurement was indicated in a variety of ways: time, length, space, amounts of things, cooking/baking

*      3/26 students indicated fractions – the topic they are currently working on

*      3/26 students indicated counting in some form

*      Unusual answers:

o   “At church, I use multiplication to figure out the number of words in a the hymns.”

o   “To figure out the video game, like if you have four players and only 2 controllers you have to use math to figure out how long each person’s turn is going to be.”

Question 3:  Why is math important? (This question had the most variety of responses.)

*      6/26 indicated some use of computation in their response

*      2/26 indicated that math is used for building: “Without math, your shelter would come out ‘lopsided’.”

*      5/26 indicated some use of measurement or knowing amounts

*      6/26 spoke about $ uses

*      1 student said it’s important for tests and 1 student indicated homework

*      7/26 students gave only 1 response

*      4/26 said math will be important for your job or when you grow up

*      7/26 students indicated it’s important but were not clear or specific about why: “need it for a lot”; “won’t learn anything without math”

*      Unusual answers:

o   “Without math, you couldn’t read music.” and the same student said, “We couldn’t do anything with steps or counting.”

Question 4: How do you think grown ups use math?

*      16/26 students somehow indicated money usages

*      9/26 indicated adults use math in their jobs and of those, 5 indicated that the skills of the job included some type of measurement

*      8/26 said that grown ups use math to help children ie: with homework

*      2 students indicated that math is used in planning birthday or children’s parties (equal goody bags, sorting gifts)

*      2/26 talked about computer programming again

*      Unusual answers:

o   “For building space shuttles, or every day objects.”

o   “I don’t know”

Conclusions:

Overall, I would say that the answers these students provided are similar to the students from the low-performing school in San Lorenzo.  These students have a stronger command of vocabulary and a broader exposure to how their parents use math (taxes, jobs) and are able to include that information in their answers.  However, there remains an overwhelming connection between math and computation as well as math and money. 

Because these students were interviewed later in the year, they had covered more topics than the previous class.  I attribute the discussions related to fractions and equally sharing to that.  I also attribute part of their knowledge and connection to measurement to that.

It seems that students best identify “what math is” with what they are currently learning or have just previously learned. 

Just don't want to lose this info!!!  So I'm posting it.

Feb. update

“I am planning to collect the following data before the next meeting …”: I need to get into ONE more classroom and collect data and analyze it before the next meeting so I can start to compare the classes and come to some more solid conclusions.

I also want to interview the three teachers.  Aija suggested I ask them the same questions I'm asking the students as it may be very telling as to why I'm getting the responses I have been getting so far!  Great idea!!!

“The most important change, or changes, I will make in my teaching practice as a result of my inquiry is/are …” If nothing else, doing this work solidifies for me the absolute necessity to help students make connections between the work they are doing inside the classroom and the work they do or will do outside of the classroom.  After listening to the other presentations last week, I heard at least 2 other scholars make that same connection.  Specifically, Aija made that connection when she was presenting her work around reading comprehension.  Students didn't "know" they were supposed to be doing something other than reading the words!  Once they knew they needed to think, their reason for reading changed.  Do we tell students about reading for enjoyment, reading to learn a new skill, doing math as a part of that new skill, doing math as a part of our daily lives, or the inquiring and thinking we do that can be found in a science lesson? 

"What I need to do before I present my inquiry in May ..." A LOT!!!  Get into both of the the other 2 classes.  Interview a few students more in depth!  Think about what next steps will be as I reenter the classroom next year - what will I do differently as a result of this learning?  What will it look like in my classroom?  What will it look like as I work with my colleagues?  What might it look like as I continue to present at conferences?  In fact, what impact does this information have NOW as I prepare my presentation around fractions @ CABE in a month????

Food for thought!

Looking at my data - class 1

I have interviewed 25 students in the first of three fourth grade classrooms.  I am at the point of looking at and thinking about what the data tells me.  Thanks to Dina for helping me to figure out a way to organize it on Saturday!

Here are some overviews of what I am discovering and some thoughts around this:
Question 1: What is math?
Overwhelmingly, the students identified computation (+, -, x, /) as what math is (over 1/2 of the students).  7 students identified numbers as being part of math.  And 4 students identified math as being related to solving problems.  A few students included a connection to buying and/or making change in outside of school life, and 2 students said that doing math is like being a scientist.

I wasn't surprised that students identified computation with math.  I was surprised that so few students identified solving problems as math.  I was also surprised that only 1 student included any other subtopics in math besides computation (fractions, measurement).  The 2 students who identified math as being like science both explained it's because they answer questions.  I thought that was interesting and will be curious to see if a science connection comes up in either of the other 2 classes I'll be visiting.

Question 2a: How do you use math at school?
Again, nearly 1/2 of the students identified some kind of computation as how they use math at school.  7 students equated using math at school with what the teacher teaches or learning something.  And, 4 students identified it as solving or working on problems. 

No students talked about specific day to day school tasks that may involve math, such as taking the lunch count or attendance.  When I interviewed the initial 6 students, those types of tasks were discussed.  It seemed to me that most students in this class understood math as being "done" only during their math period and not necessarily stretching out into other subjects throughout the day.  Deeper interviews with 2 focal students in this class will help me get a better understanding of this.

Question 2b: How do you use math away from school, such as at home?

Sixteen students identified that they use math at home by studying, practicing, or learning in some way.  Of these 16 students, 3 students specifically identified that a parent helps them with this, either directly by quizzing them or indirectly by purchasing math practice books for them.  One student said he used math by playing board games and money games.  Does this mean that many students are not playing board games at home or that they're not making the connection between board games and math?  Something to consider and ask about!  A different student identified that she uses math by helping her brother with his train tracks so that he knows he has enough pieces to create the shape he wants.  Only 1 student identified using math for making purchases.  And 1/3 of the students identified some kind of computation involved.

Question 3: Why is math important?

Students seemed to have interesting ideas as to why math was important, and most students indicated more than 1-2 reasons.  6 students talked about money and making change with several indicating that you could lose your job if you can't make the right change.  8 students said you'll need math in your job.  Outside of money, one student indicated that, for example, in a construction job, you need math to calculate the amount of wood and other supplies you'll need.  14 students indicated math is important to learn and get a good education with several indicating you can't go to college without math!  The most unusual response I received to this question was, "You need math to be able to ask and answer questions, like if the police catch you."  I did not delve further into this answer...sometimes it's better to not know!

Question 4: How do you think adults (your parents, grandparents, teachers) use math?

Thirteen students talked about money, making change, shopping, and/or paying bills.  5 students said adults use it for studying.  4 students said for measurement, with 1 student specifically stating measuring fabric and another student stating his father uses measurement in his job and his mother uses measurement when she cooks.  A couple of student alluded to the adults not knowing the math and having to check the book and/or get the answer sheet.  One student said that the adult uses math when sorting the laundry!  This one made *me* think!  And, sure enough, grouping by attributes is certainly math I remember teaching my kindergartners.

Overall, I think I got mostly responses I expected.  I was hoping that these students would have a clearer picture of how math is important in their daily life.  When I spoke briefly with their teacher, she told me that she does not discuss those connections for them, so I'm thinking that unless they're referred to in their textbook, they are not being instructed in the daily connections.  She then said, "You know, maybe I ought to make those connections for them."  Yes!!!!  I will have to interview or survey her more thoroughly to determine exactly how she does teach math.

I'll be interested to compare this group's answers to the next 2 classes as the teachers' styles and understandings of math are different.

This is all certainly food for thought! 

Meeting 12/6

My inquiry question is:
How can students' understanding of how math is used in daily life situations help facilitate their math learning in the classroom?

The learning goal(s) for my students is:
Students will develop a deeper understanding and knowledge of math and will be able to identify that the math they learn in the classroom has a role in their daily lives. (?maybe?)

My indicators for success:  (How would I know that students will develop a deeper understanding?)
Through an exit interview.
*A note here, I'm actually looking at this as a longer than 1 year project.  I'm hoping to lay groundwork and data of student understanding this year and THEN change my teaching next year to incorporate discussions and/or activities during math instruction that tie daily math to classroom math.  Because I will be using students in classrooms of my colleagues, I have no control over how those colleagues will teach math and whether they will incorporate discussion or activities that will deepen these students learning and understanding.*

Who are my focal students?
At this juncture, I will be interviewing fourth grade students in the classrooms of 3-5 colleagues (90-150) interviews.  These interviews will only contain 4 questions.  From the results of these interviews I will choose 3-6 students who seem particularly interesting in their responses: perhaps because they are outliers in their responses (they have a great understanding of math or a very limited understanding).


What are my data sources?
1. Student interviews - initial
2. Teacher surveys (to be done online via SurveyMonkey or related service) that will tell me about how they are teaching math & what materials they are using.
3. Follow up interviews of focal students that will go into questioning that will identify how they know what they know about math and how they may or may not be making connections in the classroom.
4. Possible teacher survey @ the end of the year.
5. Exit interview with focal students OR perhaps a written exit survey of all students - still working this out.

HW 12/1/10

Happy December!  And.....a month to say goodbye to 2010....  (just waxing a little nostalgic this morning).

“The area I want to work on before the meeting, and at the meeting is …

 I needed to get my question DOWN!  And I have done that  - many thanks to Claire for talking me through my sticking points.

“What I am thinking right now about this aspect of my inquiry is …

Now I need to organize myself to interview students; I need to contact my friends/colleagues to set up visitations to start interviewing their students; I need to write survey questions for the teachers to fill out; and I need to set up a SurveyMonkey questionnaire with those questions....

And then, we'll see where student responses take me.  It's a wild math ride!

One last comment:  I found this book in the library last week:  http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470437758.html

I haven't started reading it yet, but picked it up because the title seemed SO pertinent!  Will follow up with my thoughts on it after I've begun (or finished) reading it.

See you all on the 6th.... 

11/15 - Meeting

At this moment in time, this is what I'm thinking of my question right now:
UH!!!!  Yikes....so I'm kind of not there now.  I was there, but some of the articles I've been reading are pushing me to think more about how kids THINK about math in every day use as opposed to making a connection between academic and after school programs.  So, maybe....hmmm.....don't know.  I'll have to get back to that one.  Also, I'm wondering more about the home-school connection and the connection between parents and teachers and how this effects students abilities to see themselves as mathematicians and/or use math daily and be successful math learners.  ARGH - too much!!! :)


Being as specific as I can be, what I want my students to learn and be able to do is:
Know that math can and how math does connect to their daily lives and how it will continue to connect to their daily lives for the rest of their lives.

I would know if my students are accomplishing the goal if I saw/heard:
Them be able to talk about the different subgroups of math and identify how they may be able to use these in the future in a career or how a grown up they know NOW is using these skills in their daily life.  For example, be able to identify that their mom uses fractions when measuring amounts for cooking and be able to be specific about how that happened.


I can find out if they are doing this by collecting:
I would say that interviewing them and/or hearing conversations from students about how math is used in places other than school.

What am I thinking now (after small group meeting)?
How can children tie real, every day math, to the learning they do in the classroom so that they can be life long math learners?
- OK, so I'm not in the classroom...what will this evidence look like?  I think that I want to continue to survey students but do a pre- & post- type survey where I ask them about their thoughts about math (see blog post from 11/3) and after they work on the Family Math activities, with the connection to every day life made clearly @ every lesson, post survey them and see if their ideas and understandings about math have changed.
Given the transiency of the students at the school, I will need to go back & interview more than the 6 students I've already spoken with.  I also wonder if the 3 grade levels is sufficient, or should I add in 2nd graders?  Adding the 2nd graders may be of interest because it's a broader age range and that may lend to a learning of how math understanding and connection to daily life changes with age.  Or it may just muddle the waters.