Student Projects

Family Math

Author: Kristin Komatsubara

Grade: 6th

Subject: Math

Family Math table particapants
Family math: Working out card problem
Family Math: foot figuring problem
Family Math: Working at four in a row table
Family math problem worksheet
Close up of family math problem

Bridging the Gap:

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 are insightful and informative. Parents helped me to see each student in a new light. Although I have expertise in teaching, parents are experts on their children.
A few years ago, it occurred to me that families are untapped funds of knowledge that could support student learning outside of the classroom. My idea seemed fundamental, yet 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 home and school gap.
Since I began my implementation of 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.
While Family Math has yielded great results, nothing is perfect, and I continue working to improve this strategy to suit the needs of my students and their families. 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, Manuel and his mother enjoyed working together at the various math stations, but found “The Card Problem” most engaging. Although they were unable to complete the entire problem, they promised to continue solving the problem at home. The week after Family Math Night, Manuel’s mother returned with him 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 with each other by sharing math learning together.
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 passively 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 guide student learning. 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 an open-ended problem of the week which 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, students teach their parents the problem of the week for homework. 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.
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 problem of the week homework, there’s a space on the homework for them to initial and 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 and/or better understanding of the concepts involved.”
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:
  • What do you need to find out?
  • What information do you have?
  • Why did you predict the answer will be 16?
  • Tell me how you’ve organized your lists of PIN codes.
  • Could the PIN start with zero?
  • Did you check to make sure that you didn’t write any code twice?
  • Can you explain how you arrived at the answer of 24?
  • Do you see any patterns in your work?
  • How confident are you of your answer?
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.
 
Sometime in late October or early November, I host “Family Math Night,” an event designed to introduce parents to the in-school math curriculum and help launch home participation in Family Math.  Family Math Night usually lasts between two to 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 know, such as a Connect Four board for multiple players. Others are open-ended challenge questions inspired by problems and activities I’ve 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!
Parents consistently voice strong appreciation for Family Math Night. Nicole’s mom is a single parent who works two jobs. She explained that Family Math Night helped her to realize that she could help Nicole 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.
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.

Fair Game A sample family math activity.


Family Math Flyer Sample of the flyer Ms. K. distributes to students to invite families to attend Family Math Night.


Bead Patterns Activity A sample Family Math activity.