The Great American Homework Battle

* Just a quick Hacking your Education update: one of the tips Dale Stephens suggests in Hacking your Education is reaching out to an expert. I recently reached out to Denise Clarke Pope, a Stanford professor, author of a Overloaded and Underprepared and Doing School: How we are creating a generation of stressed out, materialistic and miseducated children, and one of the founders of Challenge Success, an organization that partners with schools and families to provide kids with the academic, social, and emotional skills needed to succeed now and in the future.


And…….. She actually got back to me! I just wanted to chat about her experience and research on revolutionizing education in order be more focused on the “whole child.” She said she’d be happy to meet me for coffee. Unfortunately, she wasn’t back in her office at Stanford until after I left on my journey to Maine. BUT, in our various email correspondences, she introduced me to a colleague of hers from Challenge Success who is also moving to Portland, Maine. So now the plan is to get together with him once we’re both settled.


Okay, so the Great American Homework Debate.

math fractions

I’ve been coming across a lot of articles/entire books lately on homework and whether or not it’s A) important B) effective and C) good for students & families.

The beliefs on this topic are pretty polarizing and people tend to get pretty heated about it. Some educators believe that homework should be assigned nightly. Others believe that homework should only be assigned when it’s meaningful and necessary. And still others believe that there should be no homework assigned at all.

Most of the evidence indicates that homework, at least for elementary school students, is ineffective. Research shows that it does not improve their grades, their intelligence or their performance in school. As students transition into middle school and high school, small amounts of homework are valuable only if they are manageable and well thought out assignments.

But even with the well documented evidence, many arguments for, and questions about, homework remain. For example:

  • Homework keeps kids out of trouble after school
  • If all the other kids are doing homework, my child will get left behind
  • Homework is a good opportunity for parents to spend time with and help their children
  • If work isn’t completed in class, after school is a good alternative
  • Etc, etc, etc.

There are counter points to all of the above arguments. I have to say that many of the anti-homework arguments I’ve come across are incredibly compelling. I am sold on the “no homework” thing and I’ve happily provided some resources in the Resources section that have guided me to this perspective, including The Case Against Homework. This book is written by two women who present a solid argument for less homework based on research, interviews and their own experience as parents.  That being said, I also know that a lot of teachers are either required by their schools or districts to give certain amounts of homework or urged to assign homework by parents who think that without it, their children will fall behind. Again, this is a touchy subject!

Jo Boaler tackles the great homework debate in Mathematical Mindset by providing some very practical examples of how to incorporate math skills practice or reflection into kids everyday after school routine. To round out my commentary on Mathematical Mindsets, I’d like to share a few of her ideas on making homework more effective and less likely to make you (parent) or your children want to scream HELP! and ask for your evenings back.

Here are three examples:

1. “Finding math in real life” assignments. This can fit into any mathematical concept and can often be quite interesting and even fun for students. Let’s say you’re studying Area. Students might be asked to measure their backyard or kitchen, find the area and then explore how many different ways there are of creating that area using different sets of numbers. Sort like this:


This example also allows students to discuss and share their findings the next day in class.

2. Math reflection sheet. Students are given a few questions each night (or a few times a week) and asked to reflect on their successes or challenges in math. The questions can vary but may look something like this:

  • What strategies did you use to solve your equations? (pictures, graphs, cubes, number equations, math talks, etc)
  •        What was one challenge that you faced and how did you overcome it?

3. Have students create one or two problems similar to a problem that they solved in class, except a little more difficult. They can either solve these problems themselves or swap problems with another student the next day as a class starter activity.

These examples of meaningful homework are specific to math, but #2, the reflection sheet, can be cross curricular. Reflection questions get students thinking about their thinking and learning, which in turn helps them with critical thinking and verbal explanation skills.

For all of the teachers and parents out there, what are your thoughts on homework? Feel free to share any memorable, meaningful homework assignments that you’ve given or that your child has received.

Up next: My tentative career plan for when I arrive in Portland, Maine, and the steps I’m taking to set myself up for success.

-Mrs. Sanford

Revolutionizing the math class

Okay so you’re working to create this growth mindset (see last post) among the students in your class (or your child at home), now what?

The next topic from Jo Boaler’s Mathematical Mindset that made an impact on me was how desperately we need a math education revolution in the US. Our students are consistently scoring below average in mathematics, according to PISA (Program for International Student Assessment), but more importantly than that, we’re creating an army of students who loathe and fear the subject.

pisa scores

This chart is from the 2012 assessment, but we dropped even lower in math on the 2015 assessment. Andreas Schleicher, director for education and skills at the OECD, which administers the PISA exam explains that “[US] Students are often good at answering the first layer of a problem in the United States, but as soon as students have to go deeper and answer the more complex parts of a problem, they have difficulties.” 

Let’s examine how we could encourage our students to “go deeper” in math.

Jo Boaler defines math as “a set of ideas, connections and relationships that we can use to make sense of the world.” At it’s core,” Boaler continues, “it’s about patterns.” Does this sound like the math you learned in school? Or if you’re a teacher, does this sound like the math that you’re teaching?

If I were to ask my middle school students, “What is math?” I bet their definition would be more like “math is a bunch of disconnected, seemingly irrelevant formulas taught to students so that they can solve problems that they will never face in the real world.” Or some of them might even just define math as “torture.” That’s how I would’ve defined it in school.  

Math, as a subject, is meant to involve collaboration, sense making, reasoning and connections. Conrad Wolfram, a British businessman who’s known for his work on information technology, explains that there are 4 stages of math:

  1. Pose a question
  2. Go from the real world question to a mathematical model
  3. Perform a calculation
  4. Go from the model back to the real world to see if it solves the question

Unfortunately, according to Wolfram, much of school math is spent in stage 3: performing calculations. Not only are calculations done individually in class, but dozens are sent home for kids to practices these “skills” for homework (we’ll get into the Homework Battle another time).

You can find Wolfram’s TED Talk: Teaching Kids Real Math with Computers here

So basically we sit kids down, teach them the formula (ie: how to divide fractions) then give them a bunch of calculations to perform individually, maybe sometimes throwing in some group work or “real world” word problems.

No wonder all of the fun, creativity and curiosity is stripped from the subject.

We know it’s wrong and bad for our kids, but what are some things we can do about it?

First, we can work on redefining math (make sure the activities in class actually fit the definition from above) and try to build that growth mindset of mistakes do not = failure.

Let’s assume you’re already working on that. Here are some ideas from Boaler’s Mathematical Mindset

  • Group work, group work, group work – showing students that math is a collaborative subject meant to be a combination of questions and ideas and trial and error, this also allows teachers to weave interpersonal and teamwork skills into class. I did a few big group projects in math last year. One was a “city building” project where the groups had to work together to plan their own city using specific sizing criteria (ie: the homes must be at least 1/4 the size of the courthouse). It was so cool to see what the kids came up with. Not only did they love the project, they worked collaboratively and some even went on to add infrastructure such as a city-wide bike lane, solar panels and , of course, Starbucks. 
  • Number Talks – Pose a question, and have a discussion about ALL of the different ways that students solve the problem.
    • Here’s an example of Jo Boaler doing a number talk with a group of students. 
    • Here’s another: 18x5 show your workSee all of the different ways these students solved for the same equation? This validates each student’s process and allows other students to recognize that there are many ways to get to the same answer. It also just gets kids talking about math – rationalizing and explaining HOW they got to an answer – which is immensely beneficial to reasoning skills. Talking about these methods allows students to form a deeper understanding of multiplication, addition, subtraction and division, as well as patterns. Number talks turn numbers from abstract to concrete.

(Unfortunately, I came across Boaler’s book too late in the school year so I didn’t have a chance to try these out with my math class, but a colleague started incorporating them into her class and she reported that otherwise very uninterested kids were leaning in and sharing their ideas. She also recommended that I look into Cathy Humphrey’s book, Making Number Talks Matter)

  • Meaningful homework (or NO homework!) – Boaler places value on math reflections as homework (or exit tickets). This adds a metacognitive aspect to math. Reflections allow students to think about HOW they think about the concepts they’re working on. Here’s an example of a sheet of math reflections. She also suggests homework ideas such as:
    • Find an example of the Fibonacci sequence at home or outside
    • Find examples of other patterns at home or in nature
    • Create a problem similar to the ones you worked on in class
  • Encourage students to share their answers in multiple representations (words, graphs, tables, symbols, diagrams, etc) – An example of this is in the Featured Image on this post. Sharing multiple representations allows students to better visualize the concepts, as well as see that if one way doesn’t work for them, there are many other methods to try. Boaler shared that she often tells students: “What I really like to see is an interesting representation of ideas or a creative method or solution.”
  • Aim for “Low floor, high ceiling” questions and activities. “Low floor, high ceiling” means that everyone in class can access the ideas, yet it can be taken to high levels for the more advanced students. If students “finish” the question or activity, ask them to create a similar problem but make it slightly more difficult. Here’s a Low Floor High Ceiling example called “Paper Folding”:
    • Instructions – For each part of the problem, start with a square sheet of paper and make folds to construct a new shape. Then, explain how you know the shape you constructed has a specific area.
      1. Construct a square with exactly ¼ the area of the original square. Convince yourself that it is a square and has ¼ of the area.
      2. Construct a triangle with exactly ¼ the area of the original square. Convince yourself that it has ¼ of the area.
      3. Construct another triangle, also with ¼ the area, that is not congruent to the first one you constructed. Convince yourself that it has ¼ of the area.
      4. Construct a square with exactly ½ the area of the original square. Convince yourself that it is a square and has ½ of the area.
      5. Construct another square, also with ½ the area, that is oriented differently from the one you constructed in 4. Convince yourself that it has ½ of the area.
  • Prepare students to be convincing. Ask students to first convince themselves that they came up with a reasonable solution (pretty easy to do – convince yourself that what you did is correct), then have them convince a friend (a bit more challenging), then finally have them convince a skeptic (this involves lots of explaining and showing of how they came to a solution and it also builds reasoning skills).


These are just a few of the many steps we could take in the direction of sparking a mathematics revolution in the US. By shifting our focus and aiming towards a more dynamic, interactive, deep, creative and collaborative subject, students will hopefully start to show more interest and be more engaged in math class.

-Mrs. Sanford

Fire those synapses

Hi. Mrs. Sanford Speaking.

I hope everyone had a fun and festive 4th of July. The great thing about a Tuesday 4th is that there’s a very long weekend followed by a very short week 🙂

Anyways, back to summer reading.

Another book I’m currently reading is Mathematical Mindset by Jo Boaler. If I were to tell my past self that I’d be thoroughly enjoying a book about Math, my past self would have a heart attack. I’m not just enjoying the read though, I’m gobbling it up, and telling friends about it, and taking notes, and digging into all of Boaler’s tangential resources (many of which I’ve shared in the Resources page). And I’ll tell you what, it is changing my views, not only on math education, but also on mindset and on homework. There is so much packed into this book. In this post, I’m going to focus only on the Math Mindset piece. “Revolutionizing Math Education” and the “Homework Battle” will come later.

Let’s begin with just a little overview of the book. In Mathematical Mindset, Boaler explains that, despite what is commonly believed and what people often say, there is no such thing as a “math person” or a “math brain.” On the contrary, we all have the ability to learn high levels of math. Boaler says “We need to free young people from the crippling idea that they must not fail, that they cannot mess up, that only some students can be good at math…” (Boaler, 2016). She gives examples of how to open up problem sets in math to make them more meaningful and accessible, as well as techniques to change the language we use and the classroom culture from one of fearing mistakes to one of embracing mistakes. There is also a huge Appendix in the back that provides many wonderful examples of the ideas and exercises that Boaler explains in the book. This resource isn’t just for teachers though. I know a hand full of parents who say that reading this book is just as beneficial with their approach to parenting as it is in directing their teaching in class. 

So…. Mindset!

Carol Dweck, a friend and colleague of Boaler’s, and the author of the forward of this book, is a leader in the discussion on the power of Mindset (you may recognize her name from my first post about Summer Reading). According to Dweck, there are two different types of mindsets: Fixed Mindset and Growth Mindset. You can find a more detailed definition on Dweck’s website, Mindset online, but here’s a quick synopsis in regards to math:

  • Kids (and adults) with fixed mindsets believe that they are either good at math or bad at math and that very little they do is going to change that. For example, someone who has never really thrived in math may believe that he is just “not a math person,” when really he just hasn’t been given the opportunity to connect with math in a meaningful way. People with fixed mindsets believe that mistakes are bad. They are often terrified of making mistakes because they fear that making mistakes will result in them being labeled as stupid.
  • Kids (and adults) with growth mindsets, on the other hand, believe that intelligence grows and that the more they learn, the smarter they become. They are encouraged by mistakes because, as Boaler points out, mistakes make synapses in our brain fire, resulting in brain growth.



“A lot of evidence suggests that the differences between those who succeed and those who don’t is not the brains they were born with, but their approach to life, the messages they receive about their potential, and the opportunity they have to learn” (Boaler, 2016).

People aren’t born with these mindsets, they are learned. They’re learned by experiences with teachers and schools, exposure to language, observations of parents and friends, etc. Schools, unfortunately, often perpetuate the idea of fixed mindset by grouping students into high and low levels, by giving monotonous worksheets filled with problems with only one right answer, and by grading based on the number of mistakes made on assignments and tests. Fostering a growth mindset in students takes a lot of work. Boaler provides ample examples of ways to change your language and change the nature of your class (or home life) to foster this growth mindset.

One idea is to use language such as “It’s great that you’ve learned that” or “I love how you’re thinking about this problem.” These are two examples of praising what the students have done and learned, instead of praising them as a person. Notice the difference between these responses and “You are so smart.”

It may not seem problematic to tell a kid she’s smart. In fact, it seems kindof nice, right? People love hearing that they’re smart. The problem is, labeling someone as “smart” often puts so much pressure on the kid to stay “smart” that they are terrified of making mistakes and losing their status as “smart.” Research shows that kids who are labeled as smart by parents or teachers choose to do less rigorous work in order to not fail, because failing would take away their “smartness.” Whereas kids who are praised for their determination and grit chose to attempt more difficult work. What do we want to value, kids who are afraid to take on the challenge of more difficult problems just to maintain their status as smart, or kids who are continually willing to challenge themselves and recognizing that their effort is paying off?

Another example in the book that Boaler gives as the type of language that she uses with her students is: “Do you know what just happened? When you got that answer wrong, you’re brain grew.” I love how she’s flipped that around and turned mistakes into fabulous learning and growth opportunities instead of failures to avoid at all costs. 

Changing your language in order to foster a growth mindset is not easy. I tried to be mindful of the language I was using with my math students at the end of this school year, and I noticed that I often used phrases such as “Look at you! So smart!” I made a concerted effort to change these messages to ones where the kids were able to recognize their own hard work and effort on tasks. I had the pleasure of witnessing my colleague, who was also reading Mathematical Mindsets, implement many of Boaler’s strategies a little bit earlier in the school year, and it was really fun to see the difference in the attitude of the kids in her class. 

This mindset and language aspect of the book really struck me because I was one of those students who said “math just isn’t my thing” and I grew up absolutely accepting that I’m just not a “math person.” It’s one way of writing off a failure or briefly explaining away a weakness. And it’s a perfectly accepted excuse in this day and age. All the time, I hear teachers say to students “It’s okay, math was never really my thing, either – you just have to get through it.” What kind of message does this send to kids?

Evidence suggests that this attitude and language among teachers, especially female elementary teachers (which make up a very large percentage of that subset), is a major contributing factor for why young girls lose interest in math. We should all be working extra hard to reverse the downward trend of women and girls in STEM disciplines.

I’m not sure I’ll ever teach math again (remember, I’m in a big transitional phase), but encouraging a growth mindset is cross-curricular. Wherever the future brings me in my teaching career, I will be sure to start off with heavy growth mindset building and strive to practice better language and encouragement with the kids. Mathematical Mindset provides much of what you’d need in order to preparation for this type of setup. 

Boaler provides many ways for teachers and parents to build student’s growth mindsets in class and at home. Here are her 7 “norms”:

positive norms

Another example is that she likes to start classes by telling students what she values and what she does not value:

I value

  • displaying your work in multiple different representations (graphs, pictures, charts, sequence, color coding, etc)
  • deep thinking
  • the ability to explain your thought process and your answer to a skeptic
  • questions and mistakes

I do not value

  • speed*

*speed is often the measure of ability in math. Kids who quickly solve math equations are thought to be smart. Boaler stresses that it is important to praise deep thinking and discussion over speed, and giving open ended problems instead of simple equations naturally encourages deep thinking and discussion.

albert einstein

The mindset aspect is integral to Boaler’s approach to successful mathematics experiences. Check out this quick video that Boaler made with some of her grad students at Stanford. 


I can’t express how incredibly resourceful this book is. It’s packed with “Aha” moments and I believe that if it was required reading for all math (and other subject) teachers, kids would be more confident with their abilities, more competent in their problem solving skills and the US would not be 35th in the world in math scores.

There are a few more links to some amazing resources from Boaler and her Stanford YouCubed organization on the Resources page, such as videos, activities and some online professional development courses. Check ’em out.

-Mrs. Sanford



Mindset chart created by Reid Wilson; icon by

Education Hack

Hi. Mrs. Sanford speaking.

One professional/general life development book that I’m currently reading (and loving) is Hacking your Education by Dale Stephens.

I first heard about this book a few years ago when I came across UnCollege in SF. UnCollege is a gap year program that focuses on mentorships, real world experiences and allowing students to take ownership over their education. The founder, Dale Stephens, wrote this book as a guide to reclaiming education and showing people that you don’t necessarily have to go the traditional route of high school –> college –> professional world in order to be successful. Although I bought the book a few years ago, I’m finally getting around to reading it.

Stephens’ book is very practical, and it not only has some great ideas on self-directed learning but it also has a solid message. He isn’t claiming that college is bad or wrong and that no one should suffer through (or enjoy!) 4 years of traditional college education; he’s pointing out that this route is not for everyone. What else could you have done with 4 year’s worth of time and $40,000-$150,000? Stephens describes his experience in school and how he became successful after dropping out. He also describes dozens of other examples of very successful people working their way into their dream jobs by networking, volunteering, taking classes independently, showing their work to the public and building up real life experiences that are valuable resume builders.

Some very direct advice and exercises in the book that resonated with me are :

Finding a mentor – look for someone who is already really good at what you want to be good at, young or old, and reach out to them. It never hurts to send an email asking to buy someone coffee.

Waking up early

hack wake up call

Making “To-Do” lists (and “To-Learn” lists) – be very specific about your To-Dos and find an “accountability buddy” with whom you can rely on to help keep you on track.

Forming collaborative learning groups – Whether it’s politics or cooking or learning French, find others who share your interest (you can find groups online or form your own with friends or acquaintances) and get together to learn and discuss.  

Volunteering – This is free work for the employer and valuable experience for you. Stephens’ even offers this example email to get you started:

hack volunteer letter

Creating a personal website or blog and WRITE (which is largely where the motivation for this blog came from) – Get your thoughts and your work out there! Some examples of easy set-up website platforms are WordPress, and Tumblr.


What I like about Hacking your Education is that Stephens is showing (and telling) that college is not the only way to success and happiness. Although the college bit is totally irrelevant to me (I’m way past that), having worked with students who struggle with learning differences, I understand how incredibly important it is for this message to be delivered: You Have Options. You Can Choose.

Yet it’s not just a message for students with LDs. Student needs and learning styles aren’t always accommodated in traditional academic environments, leading to frustration, boredom and often failure. This failure does not predict their future potential. I’ve known dozens of students who thrive in coding or engineering or art but have low self esteem because they aren’t “good” at school. These kids need the message as well. You Have Options. You Can Choose.

Again, though Stephens’ book is about hacking your education, it has still been a really valuable read, even for someone who has a Master’s degree. Here are a few things it’s inspired me to do, as well as a few things I absolutely plan on doing. I’ll follow up with these to-dos later.

I have:

  • Started writing more
  • Set up a blog
  • Made a list of things I want to learn (my list is at the end of this post)

I plan to:

  • Do the “52 Cups of Coffee” challenge *
  • Reach out to the city Sustainability Coordinator in Portland, Maine about volunteer opportunities

* 52 Cups of Coffee is an idea started by Megan Gebhart where you buy a cup of coffee for ,and sit down with, one person every week for a year. The first person suggests the second person, the second person suggests the third person, and so on.

While reading Hacking Your Education, I’ve come across many other resources that point to the same message. For example, in The New York Times daily digest the other morning, I came across a relevant article on Tech companies valuing skills over college degrees. You can find that article on the Resources page. There is also a link to a beautiful spoken word video by Suli Breaks entitled “Why I Hate School but Love Education.”

Okay, here’s my “To-Learn” List:

  1. Learn the basics of Microsoft Excel 
  2. Learn how to make (delicious) Sauerkraut that doesn’t just taste like salt
  3. Learn how to use WordPress with more ease

What’s on some of your “To-Learn” lists?

-Mrs. Sanford

*Want more “Hack”? Check out the Resources page for Dale Stephens’ TED Talk, a story on NPR, a link to his book, and more.

Summer Reading

Hello. Mrs. Sanford speaking.

This is a transitional time for me. I just finished my third year of full time teaching at a private school in San Francisco and my husband and I are about to make a big move east for two reasons:

  1. To be closer to our families
  2. To be able to buy a house for less than a million dollars

From here

San Francisco, CA, USA

To here

Lighthouse in Portland Maine In Fort Willams Park

Teaching in SF has been a wonderful experience. Not only was I lucky enough to have been employed by a school which allowed me to create my own curriculum and run my classes with my own vision, I was also surrounded by many incredibly competent and talented educators and administrators. These educators have been friends and mentors to me. The Bay Area has also provided me with ample opportunities to expand my educational horizons by supplying a wealth of innovative pedagogical resources and tech-oriented learning. For this I will be forever grateful. I will also strive to carry this forward thinking approach with me wherever I go.

As I enjoy my last summer vacation in SF and begin my transition east, I’m setting aside some time for professional development. I have a list of self assigned summer reading, as well as a few training workshops. On this blog I’ll be sharing my thoughts on and experiences with these books and trainings (among other resources I come across in life). I’d love to know what others are reading and doing this summer in order to advance their knowledge of education and teaching practices. So please comment and share your thoughts and ideas.

Here is my summer reading list:

  • Mathematical Mindset by Jo Boaler
  • The New Art and Science of Teaching by Robert Marzano
  • Mindset: The New Psychology of Success by Carol Dweck
  • Teach Like a Champion by Doug Lemov
  • Hacking your Education by Dale Stephens

And of course a few non-education related novels just for fun:

  • The Baklava Club by Jason Goodwin (This is the 5th volume of Goodwin’s Ottoman detective series – so good!)
  • The Little House on the Prairie books by Laura Ingalls Wilder (because I’ve never read them and because my husband talks about them a lot)


  • Making Math Real Overview
  • Wilson Reading

Many of the trainings I have done and will be doing are aimed towards students with mild to moderate learning differences or with language based learning disabilities such as dyslexia. This is because that was the focus of my school and the profile of the students with whom I worked these past three years. But I believe that these resources and techniques can be incredibly beneficial to all students.

I completed the Making Math Real Overview in early June. This is a great math program that focuses on making math into a more concrete subject for students who struggle with the abstract aspect of the subject. There are lots of techniques for visualizing problems and, as the name suggests, “making math real.” I enjoyed the overview; however, I got a little tired of hearing questions answered with “Oh, you’ll learn that in the content courses.” 

The two books that I’ve started (and almost finished) are Hacking your Education and Mathematical Mindset, both of which I will discuss more in the coming posts, so stay tuned.
books for blog

– Mrs. Sanford