“I was teaching my mom and it was so cool!”
Half an hour before school, Katrina excitedly explains how she solved this week’s home math assignment with her mother. Traditionally, math homework does not generate much enthusiasm, but the implementation of Family Math in my classroom has helped me, my 6th grade students, and their families enjoy learning math together.
I’ve always enjoyed working closely with my students, but in recent years I’ve become most interested in my interactions with their parents. As a middle school teacher, I manage multiple classes, and trying to find time to meet with individual families has always been challenging. However, the conversations I have with parents help me to see each student in a new light. Although I may have expertise in teaching, parents are experts on their children.
A few years ago, it occurred to me that families are untapped sources of knowledge that could support student learning outside the classroom. My idea seemed fundamental but foreign because I had never looked beyond the school environment. I began to research and experiment with approaches to build communication with families and engage them as education partners. The result, Family Math, is my attempt to bridge the gap between home and school.
In my math classroom, I emphasize collaborative learning where students actively co-construct knowledge. Visitors are often surprised when observing my classroom because they expect to see a teacher-centered lecture with students taking notes. In contrast, my classroom is a dynamic community with students working together to solve real-world problems and justify their responses. As a teacher, I provide feedback and act as a guide. In the end, I want students to recognize their math skills as valuable and feel ownership over their learning.
The value of Family Math lies in its ability to promote collaborative student learning beyond the classroom. Compared to traditional, isolated homework drills, Family Math home activities build a rich, social learning experience that extends the collaborative learning done in class into the home environment. Each week students are provided with a packet that includes an open-ended math problem. They are expected to share the problem with a parent or other mentor, discuss possible solutions, and then explain their solution to their mentor after they’ve completed the problem. Parents aren’t supposed to solve the problems for their children, but to act instead as inquisitive observers, asking questions that encourage students to analyze their math ideas.
Sample family math problem:
The PIN Problem: “I forgot the code! I’m ready to cry! How many arrangements do I need to try?” Ms. Morales has forgotten the code to access money from her bank account. It is a four-digit personal identification number (PIN) and luckily she remembers that it includes the numbers zero, four, eight, and nine. How many possible arrangements are there for Ms. Morales’s PIN?
Sample parent questions:
To ensure that learning at home is valued, I provide opportunities for students to present their problem solving in class each week. Since the problems are open-ended and can be solved in many ways, it is a wonderful learning experience for students to hear how their peers arrived at a solution. To reinforce the learning cultivated through these conversations, each weekly home packet includes a space for reflection where students record their classmates’ alternative strategies and reflect on their understanding of the problem.
An additional benefit of family math is that it provides an informal progress report for parents to understand their child’s strengths, needs, and interests. To ensure that parents are included in the family math activities, there’s a space on each page of the packet for them to initial. There’s also a self-evaluation page that includes space for parents to provide written feedback. In an online survey, one parent wrote, “Home assignments alert both the child and parents what areas the child excels in and what areas require improvement or better understanding of the concepts involved.”
Each year, I introduce students to the structure of Family Math by first completing similar packets in class. This allows students to familiarize themselves with open-ended problems, math discussion, the self-evaluation checklist, and the overall format of the packets before attempting them at home. When working on packets at home, I allow students to choose the mentor who will best support them in their learning. Most students choose parents, but others select older siblings, tutors, coaches, or even classmates.
Some time in late October or early November, I host Family Math Night to introduce parents to the math curriculum and launch home participation. Family Math Night usually lasts between two and three hours. It begins with a concise presentation of our math curriculum, discusses the difference between “doing” math and understanding math, and emphasizes the importance of mathematical discovery and application. Together we review family math homework expectations and discuss how parents can help support student learning at home.
Following the presentation, families are invited to experience the fun and applicability of mathematics by rotating through a variety of stations. At each station there is an interactive challenge or math game. Some of the games are relatively well known, such as a Connect Four board for multiple players. Others are open-ended challenge questions inspired by problems and activities I collected from various books, websites, and conferences. All of the stations are designed to be fun and to help families recognize that math is everywhere!
Sample Family Math Night station activities:
The Handshake Problem: With only one person in the room, there will be no handshake. With two people, there will be one handshake. How many handshakes will there be with three people? Four? Continue the pattern and describe what you notice.
The Card Problem: Using a set of 10 cards (ace through 10), figure out how to arrange the cards so that the following can happen: Turn over the top card, which should be an ace and place it face up on the table; move the next card to the bottom of the deck. Turn over the third card, which should be a 2, and place it face up on the table; move the next card to the bottom of the deck. Continue this way, turning over a card, placing it face up on the table, and moving the next card to the bottom of the deck. When you are done all the cards should be face up in order on the tabletop.
Parents consistently voice strong appreciation for Family Math Night. Jessica’s mom, a single parent who works two jobs, explained that Family Math Night helped her to realize that she could help Jessica without having to “know all the math.” It is a revelation for many families to realize that informal math challenges, puzzles, and games are available and can easily be implemented in their homes to build mathematical understanding.
Since I began Family Math, I have observed a high level of student participation. In comparison to the traditional packets of lengthy problem sets, family math has shown a noticeable increase in work completion and student attentiveness. Students are more willing to volunteer to present their solutions before classmates, and most students show interest in different strategies. Student quizzes, in-class conversations, and presentations all reveal an increase in the quality and quantity of student response. In addition, students recognize the value and connection of home math activities and classroom performance. One student, Luis, commented, “I keep working until I can mark something in each (self-evaluation) box, you know, modeling and reasoning. It’s because those are all the things I need to do on the quizzes, so I try to do them all.”
While family math has yielded great results, nothing is perfect and I continue to improve this strategy. This year, recognizing the need to balance critical thinking with facility in completing standard mathematical operations, I incorporated a section of traditional math practice after the open-ended math problem. From parent feedback, I also recognized that the relationship between parents and students sometimes becomes tense when they are unsuccessful at solving the family math problem. I’m currently working to create more options and integrate more games and puzzles, similar to the ones presented at Family Math Night. Hopefully providing choices will encourage students and families to play or do math more frequently and remove the pressure of solving the problem.
Building bridges between school and home has required a significant investment of time, creativity, and communication. However, the dividends have been enormous. At this year’s Family Math Night, for example, Max and his mother enjoyed working together at the various math stations, but found “The Card Problem” most engaging. Although they were unable to finish the entire problem, they promised to continue solving it at home. The following week, Max’s mother returned with Max and his younger sister to share their solution. This family’s experience illustrates the interest and excitement Family Math has generated. It also provides a great example of the connections families can create by doing math together.
To learn more about Family Math, visit Kristin Komatsubara’s digital portfolio at https://staff.htmnc.hightechhigh.org/~kkomatsubara. A version of this article will also appear in the forthcoming book, Learning by Design: Projects and Practices at High Tech Middle, available in May 2010 at the HTH bookstore:
https://www.hightechhigh.org/student-work/publications/
“I was teaching my mom and it was so cool!”
Half an hour before school, Katrina excitedly explains how she solved this week’s home math assignment with her mother. Traditionally, math homework does not generate much enthusiasm, but the implementation of Family Math in my classroom has helped me, my 6th grade students, and their families enjoy learning math together.
I’ve always enjoyed working closely with my students, but in recent years I’ve become most interested in my interactions with their parents. As a middle school teacher, I manage multiple classes, and trying to find time to meet with individual families has always been challenging. However, the conversations I have with parents help me to see each student in a new light. Although I may have expertise in teaching, parents are experts on their children.
A few years ago, it occurred to me that families are untapped sources of knowledge that could support student learning outside the classroom. My idea seemed fundamental but foreign because I had never looked beyond the school environment. I began to research and experiment with approaches to build communication with families and engage them as education partners. The result, Family Math, is my attempt to bridge the gap between home and school.
In my math classroom, I emphasize collaborative learning where students actively co-construct knowledge. Visitors are often surprised when observing my classroom because they expect to see a teacher-centered lecture with students taking notes. In contrast, my classroom is a dynamic community with students working together to solve real-world problems and justify their responses. As a teacher, I provide feedback and act as a guide. In the end, I want students to recognize their math skills as valuable and feel ownership over their learning.
The value of Family Math lies in its ability to promote collaborative student learning beyond the classroom. Compared to traditional, isolated homework drills, Family Math home activities build a rich, social learning experience that extends the collaborative learning done in class into the home environment. Each week students are provided with a packet that includes an open-ended math problem. They are expected to share the problem with a parent or other mentor, discuss possible solutions, and then explain their solution to their mentor after they’ve completed the problem. Parents aren’t supposed to solve the problems for their children, but to act instead as inquisitive observers, asking questions that encourage students to analyze their math ideas.
Sample family math problem:
The PIN Problem: “I forgot the code! I’m ready to cry! How many arrangements do I need to try?” Ms. Morales has forgotten the code to access money from her bank account. It is a four-digit personal identification number (PIN) and luckily she remembers that it includes the numbers zero, four, eight, and nine. How many possible arrangements are there for Ms. Morales’s PIN?
Sample parent questions:
To ensure that learning at home is valued, I provide opportunities for students to present their problem solving in class each week. Since the problems are open-ended and can be solved in many ways, it is a wonderful learning experience for students to hear how their peers arrived at a solution. To reinforce the learning cultivated through these conversations, each weekly home packet includes a space for reflection where students record their classmates’ alternative strategies and reflect on their understanding of the problem.
An additional benefit of family math is that it provides an informal progress report for parents to understand their child’s strengths, needs, and interests. To ensure that parents are included in the family math activities, there’s a space on each page of the packet for them to initial. There’s also a self-evaluation page that includes space for parents to provide written feedback. In an online survey, one parent wrote, “Home assignments alert both the child and parents what areas the child excels in and what areas require improvement or better understanding of the concepts involved.”
Each year, I introduce students to the structure of Family Math by first completing similar packets in class. This allows students to familiarize themselves with open-ended problems, math discussion, the self-evaluation checklist, and the overall format of the packets before attempting them at home. When working on packets at home, I allow students to choose the mentor who will best support them in their learning. Most students choose parents, but others select older siblings, tutors, coaches, or even classmates.
Some time in late October or early November, I host Family Math Night to introduce parents to the math curriculum and launch home participation. Family Math Night usually lasts between two and three hours. It begins with a concise presentation of our math curriculum, discusses the difference between “doing” math and understanding math, and emphasizes the importance of mathematical discovery and application. Together we review family math homework expectations and discuss how parents can help support student learning at home.
Following the presentation, families are invited to experience the fun and applicability of mathematics by rotating through a variety of stations. At each station there is an interactive challenge or math game. Some of the games are relatively well known, such as a Connect Four board for multiple players. Others are open-ended challenge questions inspired by problems and activities I collected from various books, websites, and conferences. All of the stations are designed to be fun and to help families recognize that math is everywhere!
Sample Family Math Night station activities:
The Handshake Problem: With only one person in the room, there will be no handshake. With two people, there will be one handshake. How many handshakes will there be with three people? Four? Continue the pattern and describe what you notice.
The Card Problem: Using a set of 10 cards (ace through 10), figure out how to arrange the cards so that the following can happen: Turn over the top card, which should be an ace and place it face up on the table; move the next card to the bottom of the deck. Turn over the third card, which should be a 2, and place it face up on the table; move the next card to the bottom of the deck. Continue this way, turning over a card, placing it face up on the table, and moving the next card to the bottom of the deck. When you are done all the cards should be face up in order on the tabletop.
Parents consistently voice strong appreciation for Family Math Night. Jessica’s mom, a single parent who works two jobs, explained that Family Math Night helped her to realize that she could help Jessica without having to “know all the math.” It is a revelation for many families to realize that informal math challenges, puzzles, and games are available and can easily be implemented in their homes to build mathematical understanding.
Since I began Family Math, I have observed a high level of student participation. In comparison to the traditional packets of lengthy problem sets, family math has shown a noticeable increase in work completion and student attentiveness. Students are more willing to volunteer to present their solutions before classmates, and most students show interest in different strategies. Student quizzes, in-class conversations, and presentations all reveal an increase in the quality and quantity of student response. In addition, students recognize the value and connection of home math activities and classroom performance. One student, Luis, commented, “I keep working until I can mark something in each (self-evaluation) box, you know, modeling and reasoning. It’s because those are all the things I need to do on the quizzes, so I try to do them all.”
While family math has yielded great results, nothing is perfect and I continue to improve this strategy. This year, recognizing the need to balance critical thinking with facility in completing standard mathematical operations, I incorporated a section of traditional math practice after the open-ended math problem. From parent feedback, I also recognized that the relationship between parents and students sometimes becomes tense when they are unsuccessful at solving the family math problem. I’m currently working to create more options and integrate more games and puzzles, similar to the ones presented at Family Math Night. Hopefully providing choices will encourage students and families to play or do math more frequently and remove the pressure of solving the problem.
Building bridges between school and home has required a significant investment of time, creativity, and communication. However, the dividends have been enormous. At this year’s Family Math Night, for example, Max and his mother enjoyed working together at the various math stations, but found “The Card Problem” most engaging. Although they were unable to finish the entire problem, they promised to continue solving it at home. The following week, Max’s mother returned with Max and his younger sister to share their solution. This family’s experience illustrates the interest and excitement Family Math has generated. It also provides a great example of the connections families can create by doing math together.
To learn more about Family Math, visit Kristin Komatsubara’s digital portfolio at https://staff.htmnc.hightechhigh.org/~kkomatsubara. A version of this article will also appear in the forthcoming book, Learning by Design: Projects and Practices at High Tech Middle, available in May 2010 at the HTH bookstore:
https://www.hightechhigh.org/student-work/publications/
