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.
Monday, December 6, 2010
Wednesday, December 1, 2010
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....
Monday, November 15, 2010
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.
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.
Wednesday, November 3, 2010
11/3 - Talking to kids about math
Today I went to the after school program to talk to some 3rd, 4th, & 5th graders about their understanding and thoughts about math. It was eye opening to say the least. I was expecting some "typical" answers...but alas, some children surprised me! Here are the questions with some answers:
Q 1: What is math?
DW (3rd grader): Math is something teachers do. It's numbers & digits. It's something that helps you learn about numbers.
BT (4th grader): It's addition, multiplication, division, and subtraction. You can do problems to learn more educational problems in math. You can use + & x together. Actually, you can use all computation together. For example: 6 + (5-4) =
JM (5th grader): Math is multiplication and division. It's addition and subtraction. It's fractions, geometry.
Q 2: How do you think you use math every day? At school?
CL (5th grader): In math class. She (the teacher) gives us directions for classwork. We use flash cards to play around the world.
AM (3rd grader): To solve problems with addition, subtraction, multiplication, and division. To do story problems. A story problem asks a question like "How many more apples than bananas?"
RR (4th grader): When we use numbers in the classroom, like for lunch count or to find out who is absent that day. During math time. When the teacher has us count, like for lunch count.
Away from school?
RR: My mom & dad count money, like for the bills and rent to make sure there's enough money for everything. My mom is an accounting person at a mental hospital, so she uses math a lot.
AM: In my math book from 2nd grade, last year. I have a video game about math.
CL: Extra studying of my multiplication facts, tutoring.
Q 3: Why do you think math is important?
JM: When you want to be a teacher you need to "learn all this great math" so you can teach other students.
RR: You wouldn't be able to pay bills. How would you know how your bills, pay, rent?
AM: To learn stuff, division, subtraction, addition, multiplication. To know story problems and how to fix things to get a good job. (When asked, what kinds of things would you fix with math? A: air conditioners)
Q 4: How do you think the adults in your life use math?
DW: She uses money to count it at the store.
BT: To help their kids with their homework. To buy groceries. To do the bills, "definitely bills". If the grown ups are teachers, they use lots of math.
I interviewed 6 students all together. I just wanted to have a better understanding of what the students' attitudes and ideas are about math. This reminds me that when I was working in the classroom, doing surveys and questionnaires about what they know and understand about learning and the importance of learning was very eye opening!
Q 1: What is math?
DW (3rd grader): Math is something teachers do. It's numbers & digits. It's something that helps you learn about numbers.
BT (4th grader): It's addition, multiplication, division, and subtraction. You can do problems to learn more educational problems in math. You can use + & x together. Actually, you can use all computation together. For example: 6 + (5-4) =
JM (5th grader): Math is multiplication and division. It's addition and subtraction. It's fractions, geometry.
Q 2: How do you think you use math every day? At school?
CL (5th grader): In math class. She (the teacher) gives us directions for classwork. We use flash cards to play around the world.
AM (3rd grader): To solve problems with addition, subtraction, multiplication, and division. To do story problems. A story problem asks a question like "How many more apples than bananas?"
RR (4th grader): When we use numbers in the classroom, like for lunch count or to find out who is absent that day. During math time. When the teacher has us count, like for lunch count.
Away from school?
RR: My mom & dad count money, like for the bills and rent to make sure there's enough money for everything. My mom is an accounting person at a mental hospital, so she uses math a lot.
AM: In my math book from 2nd grade, last year. I have a video game about math.
CL: Extra studying of my multiplication facts, tutoring.
Q 3: Why do you think math is important?
JM: When you want to be a teacher you need to "learn all this great math" so you can teach other students.
RR: You wouldn't be able to pay bills. How would you know how your bills, pay, rent?
AM: To learn stuff, division, subtraction, addition, multiplication. To know story problems and how to fix things to get a good job. (When asked, what kinds of things would you fix with math? A: air conditioners)
Q 4: How do you think the adults in your life use math?
DW: She uses money to count it at the store.
BT: To help their kids with their homework. To buy groceries. To do the bills, "definitely bills". If the grown ups are teachers, they use lots of math.
I interviewed 6 students all together. I just wanted to have a better understanding of what the students' attitudes and ideas are about math. This reminds me that when I was working in the classroom, doing surveys and questionnaires about what they know and understand about learning and the importance of learning was very eye opening!
Friday, October 29, 2010
11/1/10 - Thoughts on student work
1. The student work I have collected since the last meeting is:
Work from a Family Math activity called "Guess and Group". In this activity, students grab a handful of an item, like buttons, for example. Before they count how many of the item they have, they estimate how many they were able to grab. They write this number on a worksheet (which I provided) so they don't forget. Then, they count how many of the item they actually were able to grab. They write this number down. Then, they draw the actual item and group them according to the directions, by drawing circles or loops around a specified number.
This activity helps children learn to estimate in general, and specifically what they can hold in their hands. Also, the grouping aspect helps children move toward algebraic notation. For example, if I grabbed and counted 23 buttons and grouped them in sets of 5, then after I have drawn circles around all of the groups of 5, I can see that I have 3 buttons left over that can not be grouped. If I write this mathematically, I can write 23 = 4 x 5 + 3.
Generally, because my inquiry is looking at linking the Boys & Girls Club after school program to the day program & home, someone from the after school program is teaching these classes. However, I taught this one so he could see me model. I explained the mathematical notation to all of the groups, 2nd grade, and higher. One second grader was able to try this independently, and several students 3rd-5th grade moved to this step on their own. (More about that later...)
2. In looking @ the data, one thing I have noticed about how/what students have learned:
Some students seem to not have a lot of experience with estimation. This is evidenced by their guess number being the same as their actual number of items & by my witnessing this in the classroom as I was teaching. It seems that as they get older, however, their estimation skills improve. For one thing, they seemed less concerned about "guessing right" and more accepting of estimation being what it is - an educated guess. Also, the older the student the more accurate their estimate was; meaning that they may have used prior information or their estimate numbers and actual numbers were close, but not exactly the same. For example, "Edgar" counted beans first and had an actual number of 52 (his estimate had been 56). When he took his second turn, he counted something of similar size (most of the items were of similar size) and his estimate was 52. Thus, he showed me that he was using the previous actual number to help him estimate his next item. I think this is great! Of course, given that his first estimate was close to the actual number, he could have used that same number as his next estimate!
I was pleased to see several students, mostly in the intermediate grades, note the mathematical equation that would demonstrate their drawing. Not everyone did this - and in fact, it's not actually part of the directions - but I wanted to have that extension there for students who were ready for it. Everyone who wrote the equation down did so correctly. When I introduced the idea to them, I heard several "ah!"s and "oh!"s. This makes me wonder if connections are being made in their classrooms - whether teachers are blatantly pointing it out or whether they are allowing students to demonstrate the connections they are making on their own. I know that time is so precious and there is so much to teach....but I do wonder!
3. My current question is:
How can the Family Math program be used in an after school program to bridge gaps between the day academic program and home while improving student understanding in math?
4. My thoughts at this point about my inquiry are:
I am going back to the school this week to meet 1:1 with some 3rd, 4th, and 5th graders to talk to them about their attitudes and ideas around math. I really want to know what they think math is and when and how they think math is used in every day life!
I have a ton of reading to do!!!!! I've started several articles - but I'm so old fashioned! I am not accustomed to reading things on the computer, so it's taking me a while to get acclimated. I may just have to break down and print and highlight the old-fashioned way! :)
Work from a Family Math activity called "Guess and Group". In this activity, students grab a handful of an item, like buttons, for example. Before they count how many of the item they have, they estimate how many they were able to grab. They write this number on a worksheet (which I provided) so they don't forget. Then, they count how many of the item they actually were able to grab. They write this number down. Then, they draw the actual item and group them according to the directions, by drawing circles or loops around a specified number.
This activity helps children learn to estimate in general, and specifically what they can hold in their hands. Also, the grouping aspect helps children move toward algebraic notation. For example, if I grabbed and counted 23 buttons and grouped them in sets of 5, then after I have drawn circles around all of the groups of 5, I can see that I have 3 buttons left over that can not be grouped. If I write this mathematically, I can write 23 = 4 x 5 + 3.
Generally, because my inquiry is looking at linking the Boys & Girls Club after school program to the day program & home, someone from the after school program is teaching these classes. However, I taught this one so he could see me model. I explained the mathematical notation to all of the groups, 2nd grade, and higher. One second grader was able to try this independently, and several students 3rd-5th grade moved to this step on their own. (More about that later...)
2. In looking @ the data, one thing I have noticed about how/what students have learned:
Some students seem to not have a lot of experience with estimation. This is evidenced by their guess number being the same as their actual number of items & by my witnessing this in the classroom as I was teaching. It seems that as they get older, however, their estimation skills improve. For one thing, they seemed less concerned about "guessing right" and more accepting of estimation being what it is - an educated guess. Also, the older the student the more accurate their estimate was; meaning that they may have used prior information or their estimate numbers and actual numbers were close, but not exactly the same. For example, "Edgar" counted beans first and had an actual number of 52 (his estimate had been 56). When he took his second turn, he counted something of similar size (most of the items were of similar size) and his estimate was 52. Thus, he showed me that he was using the previous actual number to help him estimate his next item. I think this is great! Of course, given that his first estimate was close to the actual number, he could have used that same number as his next estimate!
I was pleased to see several students, mostly in the intermediate grades, note the mathematical equation that would demonstrate their drawing. Not everyone did this - and in fact, it's not actually part of the directions - but I wanted to have that extension there for students who were ready for it. Everyone who wrote the equation down did so correctly. When I introduced the idea to them, I heard several "ah!"s and "oh!"s. This makes me wonder if connections are being made in their classrooms - whether teachers are blatantly pointing it out or whether they are allowing students to demonstrate the connections they are making on their own. I know that time is so precious and there is so much to teach....but I do wonder!
3. My current question is:
How can the Family Math program be used in an after school program to bridge gaps between the day academic program and home while improving student understanding in math?
4. My thoughts at this point about my inquiry are:
I am going back to the school this week to meet 1:1 with some 3rd, 4th, and 5th graders to talk to them about their attitudes and ideas around math. I really want to know what they think math is and when and how they think math is used in every day life!
I have a ton of reading to do!!!!! I've started several articles - but I'm so old fashioned! I am not accustomed to reading things on the computer, so it's taking me a while to get acclimated. I may just have to break down and print and highlight the old-fashioned way! :)
Saturday, October 2, 2010
10/2/10 - Meeting
1. What did you learn from data exploration today?
Today was my first session w/Mills Scholars...and I was late. However, I joined a group of very interesting folks to listen to their ideas and look @ their data.
2. How does this connect to your area of interest for study this year?
I am working with two people who are also looking @ math, and two people who are elementary folks. There's nice overlap here. And because I'm working with the afterschool program, the group member who is looking @ working with mentors will be a nice overlap.
3. What is the current draft of your question?
How can the Family Math program be used in an afterschool program to bridge gaps between the day academic program and home while improving student understanding in math?
4. Your thoughts now?
I am really quite fascinated about what students think math is. I've been reading some research relating to middle school students and their understanding of math in their daily lives. Since the Family Math program has a component about math and everyday life, I may incorporate some of that thinking into my question.
Today was my first session w/Mills Scholars...and I was late. However, I joined a group of very interesting folks to listen to their ideas and look @ their data.
2. How does this connect to your area of interest for study this year?
I am working with two people who are also looking @ math, and two people who are elementary folks. There's nice overlap here. And because I'm working with the afterschool program, the group member who is looking @ working with mentors will be a nice overlap.
3. What is the current draft of your question?
How can the Family Math program be used in an afterschool program to bridge gaps between the day academic program and home while improving student understanding in math?
4. Your thoughts now?
I am really quite fascinated about what students think math is. I've been reading some research relating to middle school students and their understanding of math in their daily lives. Since the Family Math program has a component about math and everyday life, I may incorporate some of that thinking into my question.
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