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Case Narrative

Room 101: 8:30am
Forty-five minutes before the beginning of the school day, Beth Martin, an energetic, second-year, fourth grade teacher at Winner Elementary School was busy preparing for her first-period math lesson. While gathering materials around the room, she noticed a familiar face peering in the window of her classroom door. As Beth quickly waved one of her fourth graders into the room she noticed the welling tears in the little girl's eyes. Embracing Lena in a comforting hug, Beth gently asked, “What's wrong sweetheart?”

Lena wiped her eyes and breathed a slow, calming breath before explaining. “Last night I was trying so hard to get my homework done, but I couldn't remember how you taught us to do our two-digit by two-digit multiplication. So I asked my daddy to help me out and when I tried to explain to him what you had taught us about multiplication he said it sounded crazy. He said he had a better way to do the problem, but when he showed me, it just didn't make sense. He had me multiplying and adding all sorts of numbers up and down and diagonally. When I had to write my explanation of how I did the problem I didn't even know where to begin! Ms. Martin, I am so confused. Daddy says the way you are teaching us sounds crazy, but yesterday in class it really made sense to me. Is it crazy?”

The Teacher's Lounge: 10:15am
After an invigorating hour of teaching another lesson in the series on two-digit by two-digit multiplication, Beth was feeling confident in her students' understanding and ability to solve more difficult multiplication problems. Even Lena, who had come to her in tears hours before, was engaged, participating, and even offered to explain her process in arriving at an answer in front of the class.

Beth walked into the teachers' lounge to spend her free period correcting the previous night's homework. Her confidence and mood began to decline as she examined page after page of incomplete, incorrect math homework. In many cases, her students appeared to perform traditional algorithms not taught in the framework of TERC Investigations, a K–5 mathematics curriculum with an emphasis on mathematical relationships using engaging activities and group learning experiences that her school had adopted. She wondered where her students were learning these methods. Beth quickly hypothesized that the school's push to get parents involved in their children's homework was one cause for this confusion between traditional math and the new math taught in the classrooms. She thought to herself: While the idea of families helping with homework sounds great, is it really beneficial when it just confuses the children? What am I going to do to get the parents, students, and myself on the same mathematical page?

While Beth was contemplating this question, two colleagues, Ray Donaldson and Darlene Brown entered the lounge, threw down their mountainous stacks of papers, and plopped down into the tattered vinyl chairs. Noticing Beth's pensive look, Ray, a fellow fourth grade teacher sarcastically asked, “Beth, so what about this job could possibly have you looking so concerned?” The group giggled realizing the humor in such a statement.

“Well Ray, to name one of the hundred things, I am struggling with the new Investigations curriculum. The classroom implementation of the program is really going well. My students are progressing nicely and are obviously enjoying math. In my own experience, I have never seen such a positive student response to a math curriculum. But homework has been such a problem for my students. Just this morning Lena was really upset about her father's help with an assignment. After telling her that the math we are teaching here is ‘crazy,’ he taught her the traditional algorithm for two-digit by two-digit multiplication. She was so confused about how to solve the problem, and who she should believe.”

“Oh Beth, this is just the beginning,” Darlene Brown confessed. “This will happen every time a new program or curriculum is thrown in front of your face and you're expected to understand and implement it. Parents are rarely notified of the changes when they happen. Nor are they told about the benefits and challenges of the new curriculum or how to deal with it at home. Basically, the teachers have to spend the next few years demystifying and defending the program to parents hoping they will either embrace it or give up questioning it. By that time we are changing the curriculum again anyway. Don't worry honey, you'll get use to it.”

Ray and Darlene chuckled empathetically for Beth. Ray added, “Actually, the other day I got a note from one of the directors of the after school program down the street. I guess they're getting some questions and grief from parents because the tutors don't understand the homework, which is done during the program. This made me think that our school should extend the professional development around the curriculum not just to teachers, but also to parents and after school program tutors.”

“While they're at it, how about a course for the teaching staff on working with parents. I'm 10 years into this profession and I still don't have a handle on that one,” admitted Darlene.

“So obviously I'm not the first teacher to feel the gap between what we know about the curriculum and what parents know. Why isn't this being addressed?” Beth asked.

Darlene explained, “The problem is finding someone who'll listen and then hoping they'll act on your suggestion. When you have as many years as we do you tend to act first without asking, hoping no one will mind.”

“Well then what actions are you two taking to defend the Investigations program to parents?” Beth asked.

Ray scrunched his face in a guilty manner, “Well, to be honest I haven't done a great job addressing the issue. I guess I've just been encouraging families to attend the math nights and sending the unit letters home consistently, being sure to print them in Spanish and English.”

Darlene lightly punched Ray in the shoulder. “Oh come on Ray, you know full well those family nights aren't enough. Yeah, the attendance is great and the idea of families spending quality time together focused on academics is exciting, but is that all the parents need?”

Realizing her free period was up, Beth packed up her worn canvas bag, said her goodbyes, and trudged back to her classroom. As she passed the front office she nearly collided with the principal. “Oh, good morning, Maestra. I have been looking for you. I just got a phone call from Lena's father, Mr. Caridon, and he would like you to call him regarding Lena's homework last night. He said they were having trouble and that Lena got upset when he tried to help. I told him you would call him when you had a moment today.”

Mr. Coridan, Lena's Father
“This year I have been really happy with Lena's teacher. She really cares about the kids and wants the best for them. At the parent-teacher conference she was easy to talk to and didn't intimidate me like teachers in past years. Even her room is inviting and seems like a great place for kids to be. My only concern is the way that Ms. Martin is teaching math to the kids. Lena comes home with only a few math problems each night. It seems like half the time she is writing sentences on her math papers rather than doing the arithmetic.”

“Last night she came to me asking if I could remind her which of the digits of the left number went with which digits of the right number? I told her that whatever she was talking about seemed a bit mixed up and she first had to set the numbers up on top of each other. I thought it was rather strange that she didn't do this to begin with, so I asked her to bring me her textbook to help her figure it out. When she told me they didn't have a book I was pretty surprised. From there I just had to use the way I was taught to do multiplication in elementary school. Why is Ms. Martin teaching math skills differently from the way I was taught? Maybe it is explained in the letters she sends home each month or so, but my wife and I really don't understand them. I called Ms. Martin today to express my concerns and maybe schedule a meeting to talk about this new math program.”

Lena, Fourth Grade Student
“I really used to hate math. It is such a hard subject for me to understand. This year, Ms. Martin is teaching us a different kind of math. We get to use number cards, counting rods, interlocking cubes, charts, and lots of other things to help us figure out the problems. Sometimes when I have trouble doing a problem I use the different materials and then I can figure the problem out on my own. Ms. Martin also lets us work with other kids at our tables on different problems and projects. At first we sort of just talked a lot and Ms. Martin got annoyed, but now we have learned to actually talk about math. We talk about how we get our answers, the tricks we use, and how to help each other.”

“My only problem is that when I go home and do my homework, I sometimes forget the way Ms. Martin taught us. When I ask my daddy he acts like he has no idea what I am talking about. He takes forever trying to teach me his way of doing the problem and then I end up more confused. I feel really frustrated when this happens, but it usually gets better the next day when Ms. Martin goes over it all in class. I think I'll just stop asking my daddy for help because he doesn't know as much about math as my teacher does.”

Beth Martin, Fourth Grade Teacher
“The new math curriculum has so much potential for increasing students' math abilities and their understanding of math concepts. The TERC Investigations curriculum we have adopted focuses on collaborative work, real-life math connections, and skill reinforcement games. Of course I question some aspects of the program, but overall I have been really pleased. Unlike last year, I now feel my students are able to write and talk about math in a more in-depth, realistic way and demonstrate a more concrete understanding of how and why they are solving problems. The teacher's manual offers so much content information so I'm learning as much if not more than my students. Also, our district has offered a lot of great professional development on how to implement the curriculum in the classroom, and to strengthen our own mathematical understanding.”

“My biggest concern is how parents are being prepared to deal with the new math. A lot of parents don't understand the shift in teaching methods and conclude that it's ‘crazy.’ I don't think they realize how this attitude undermines our teaching and sends negative messages to the students. I know that Principal Ramirez has made family involvement a priority for our school and started math nights, where parents can play some of the math games we use in the classroom. However, I think parents may need to see teachers teach a lesson, or explain the Investigations approach to teaching basic concepts such as multiplication or division. Somehow we need to defend why we've chosen this program and how parents can support it in the home.”

Beth's Lunch Break: 12:30pm
“Hello, Mr. Caridon, this is Beth Martin, Lena's teacher, returning your call about last night's math homework.”

“Oh, hello Ms. Martin, thanks for calling me back. I guess Lena already told you that we had a bit of trouble with the assignment. Well actually, my issue is a bit larger than that one assignment. I am really struggling to understand this new math curriculum. Last night I showed my daughter a simple two-digit by two-digit multiplication problem setup and she stared at it with a puzzled look on her face. It was as if she'd never seen it before. In talking to other parents, they seem to have similar experiences and concerns. The kids don't even have math textbooks to refer to. I really think you are a great teacher and care a lot about your students. Lena tells us this all the time. But I am seriously questioning the math instruction that is going on in your classroom.”

“Well, Mr. Caridon, the principal mentioned that you were concerned about the homework, but she didn't mention your greater concern.”

“I didn't actually get into much detail with her. She seemed a bit rushed and quickly suggested I attend the upcoming math night as a way to get involved and learn more. Maybe that would be a good event for my wife and I to attend.”

Beth paused for a moment to think about how to respond to this suggestion: Would Mr. and Mrs. Caridon really get what they needed out of this event? What should I say?

The people and events in this case are based on real life accounts, but have been disguised to protect confidentiality.

 


 Discussion Questions

Objective I. To consider the impact of curriculum changes on parent-teacher relations and on parents' participation in homework help.

  • What is the teacher's role in explaining and defending curriculum changes to parents? What is the school's role?
  • How do you evaluate Lena's father's concerns about the new math?
  • If you were Beth Martin, how would you defend the strengths of the new math curriculum to Lena's father?

Objective II. To explore outreach activities for informing and engaging parents in curriculum changes.

  • Why aren't math nights at Winner Elementary School working as well as expected?
  • What other strategies could the school use to earn parent support for the new math curriculum?
  • What skills do parents need to participate in their children's math learning at home and how can the school promote these skills?
  • How do Ray Donaldson and Darlene Brown, the senior teachers who empathize with Beth Martin's concerns, deal with parents' confusion? How can communication among teachers and school leadership improve to find joint solutions to supporting parents?

Objective III. To gain exposure to various models of effective family math involvement.

  • Identify two or three models of family involvement in math and evaluate them based on your own experience and knowledge (see Additional Resources section).
  • Adapt one or more of these models to Winner Elementary School and explain how this model might work more effectively than the activities currently in place.

 


Expert Commentary

Marlene Kliman is a senior scientist at TERC, a nonprofit STEM education research and development organization in Cambridge, Massachusetts. Her background is in mathematics, development of mathematical thinking, and educational technology. For more than 30 years, she has designed materials and methods for bringing relevant, engaging, and hands-on math to a wide range of audiences inside and outside of school. She was one of the authors of the first edition of the Investigations math curriculum.

Most parents, whatever their academic background, recognize the importance of math for children’s school and career success; they are eager to support children’s learning at home.1 Yet, today’s parents are likely to have learned arithmetic as a set of memorized facts and algorithms, in contrast to current Common Core–aligned curricula that emphasize children developing the mathematical knowledge needed to devise and explain their own arithmetic strategies.2

The "Daddy Says This New Math Is Crazy" case suggests the need to reconcile two sometimes competing goals:

  1. For teachers to implement a math curriculum that they (or their district leaders) believe is of great benefit to children but that diverges substantially from traditional arithmetic, and
  2. For parents to support their children’s math learning and feel confident that their children are gaining a solid math education.

Below are several suggestions for achieving both goals simultaneously, illustrated with examples drawn from Nana y Yo y las Matemáticas, a program in which parents and other caregivers experience a new approach to math alongside their preschoolers over the course of a year.3 Although the program involves younger children, the parallels are many: Most parents initially harbor views that preschool math consists of little more than memorizing the counting sequence and perhaps naming shapes. And at times they question the project approach, which involves exploring shapes, quantities, patterns, measurement, and logic through play, crafts, and active games. 

Leverage parents’ mathematical strengths. Look for opportunities to identify curricular content and approaches with which parents are likely to be at least somewhat familiar. Homework assignments based on this material will offer parents an opportunity to draw on their own strengths in helping children with homework. For instance, many parents arrive at Nana y Yo y las Matemáticas already comfortable reciting the counting sequence with their young children: They count children’s fingers and toes when the children are getting dressed, steps when they are walking, and pieces of food when parents are serving a snack. Few, however, are initially aware of the importance of giving children an opportunity to match, compare, and count objects on their own. From the outset, program facilitators acknowledge and applaud the counting parents already do with children; they also suggest ways to build on this, for instance, by encouraging children to count a set of objects, mix them up, and predict if they will get the same number if they re-count. In this way, parents feel supported and empowered as they use what they already know and do as a springboard.

Make communication with parents the focus of homework. Use the school day for engaging students in learning or practicing with new strategies; for homework, ask them to demonstrate a now-familiar approach to their parents. For instance, if they are grappling with two-digit-by-two-digit multiplication in the classroom, have them demonstrate an approach to solving a two-digit-by-one-digit problem to their parents. This gives parents a glimpse of the strategies children learn at school and a basis for their reassurance that children can, in fact, carry out arithmetic computations successfully and with understanding and meaning.

In Nana y Yo y las Matemáticas, parents report that the whole family benefits when children bring home a math-related craft to share with family members or a math game to play with others at home. Through these mathematical interactions with family members, children come to solidify their understandings, and family members begin to appreciate just how much children are learning and the value of the Nana y Yo y las Matemáticas approach. 

Consider capturing children’s classroom problem solving on video. Inviting parents into the classroom might help to allay their concerns, but visits to the classroom during the school day are not feasible for all parents. With near-ubiquitous smartphones, even in low-income communities, teachers can bring snippets of the classroom to parents via occasional videos sent via text.4

In Nana y Yo y las Matemáticas, video is serving as a powerful vehicle for communicating about developmentally appropriate math content and pedagogy. Program facilitators send home one-minute videos to parents via text and use them as a basis for in-the-moment communication with parents. Nana y Yo las Matematicas Pasta Counting FingersFor example, the parent of a 2-year-old questioned the mathematical value of an activity that involved matching a piece of pasta to each finger, wondering if the child’s time wouldn’t be better spent practicing writing numbers. The program facilitator showed a video of a young child engaged in the same activity and grappling with a more-or-less comparison of her five fingers and three pieces of pasta. The video formed the basis for a reassuring conversation about the role of hands-on experiences with one-to-one-correspondence in developing number sense. The parent emerged with recognition of the value of the activity for her young child. 



Final Thoughts

Children benefit from parental engagement in their learning, and many parents want to be involved. In math, an area in which adults often bring a history of rote learning rather than deep understanding, parental engagement can be particularly fraught. If educators are to enlist parents as allies in implementing a new math program, they need to start with parents’ deep desires to see their children succeed and to play a role in helping their children achieve that success.

1 Johnson, J., Rochkind, J., and Ott, A. (2014, April 14). Are we beginning to see the light? Public Agenda http://www.publicagenda.org/pages/math-and-science-ed-2010-full-survey-results; National Center for Families Learning (Spring, 2014). Family Engagement Brief. Retrieved from http://www.familieslearning.org/pdf/NCFL_Family_Engagement_Brief_.pdf

2 National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010). Common core state standards for mathematics. Retrieved from http://www.corestandards.org/Math/

3 Nana y Yo y las Matemáticas, a collaboration between YMCA of Silicon Valley and TERC, builds upon the YMCA’s Early Learning Readiness programs for children from birth to age 5 and their parents, grandparents, and other caregivers. Nana y Yo y las Matemáticas is generously funded by the Heising-Simons Foundation.

4 Smith, A. (2015, April 1). U.S. smartphone use in 2015. Pew Research Center. Retrieved from http://www.pewinternet.org/2015/04/01/us-smartphone-use-in-2015/

 


 Additional Resources

Family Involvement in Mathematics, FINE Forum, 6, Spring 2003
This issue of the FINE Forum focuses on promising practices to engage families and communities in supporting students' mathematical proficiency.

TERC Investigations in Numbers, Data, and Space
TERC's K–5 mathematics curriculum encourages students to reason mathematically, develop problem-solving strategies, and represent their thinking using models, diagrams, and graphs.

Figure This!: Math Challenges for Families
The Figure This! website offers interesting math problems and puzzles designed for middle school students to do at home with their families.

Family Math
Family Math is an after school family involvement program that brings children and parents together to solve math problems once a week for several weeks. The program was developed by the Lawrence Hall of Science at the University of California Berkeley.

Free. Available online only.

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