Teaching Problem-Solving to Young Children

Over Spring Break, I read an awesome book called Children's Mathematics: Cognitively Guided Instruction.  It's an approach to supporting children to strengthen their natural abilities to solve math word problems 

In the context of a classroom, you present a problem to the group, give them time to solve it individually (with the option to use manipulatives if they need to model the problem for themselves), and then bring them back together to share various strategies children used (since there are many ways to solve a single problem).

The teacher doesn't actually teach anything. Instead, they simply choose problems in a very intentional way and then purposefully choose which children they want to share their strategies with the group.  

We are doing action research around this approach at my school, so I've been trying it at home with Henry to prepare for our research work. 

I make these cubes available as a manipulative. I intentionally use cubes that snap together so that he can eventually apply his knowledge of the base ten system by snapping them together, making ten rods, and then counting by ten. 

I am in awe of the strong mathematical base he has built in his Montessori classroom the past three years (PK3, PK4, and kindergarten). We have done some problem-solving at home over the years ("After you wash the strawberries, will you count them and see how many each of us will get?"), but I am blown away by what he is able to do. 

Today we did the 8th type: Part Part Whole - Part Unknown. The problem was "There are 21 sour candies in a jar. 8 are pink and the rest are green. How many green sour candies are in the jar?" I changed the candy to sour patch kids because Henry loves those, and I changed the colors to reflect the colors he had in his box of manipulatives. I thought this might be the problem to stump him! It's so hard! Instead of getting stumped, he reverted to a lower level of strategies. For many of the previous problems, he was using the "counting on" strategy where he wasn't  using the manipulatives to model the problem. He was starting with one set and then using his fingers to add the second set. However, because of the difficulty of this problem, he had to resort to direct modeling. The most interesting thing was that he had to resort to very direct modeling. He used red cubes for the red candy and green cubes for the green candy. Even though I did change the problem to reflect the colors that he had in his box, I didn't mention to him that he might want to model it that way. He did it on his own. CGI says that children are natural problem-solvers, and it is so cool to watch it in action!

There are 14 different problem types, and you can increase the difficulty of each problem by adding digits to the numbers. Here are the 14 problems I'm systematically working through with Henry to see what he can do and what we should focus on next:

Problem Type	Pre (Grades K-1)
JRU (Join Result Unknown)	_____ has 24 M&Ms. _____ gave him 7 more M&Ms. How many M&Ms does _____ have now?
PPW-WU (Part Part Whole- Whole Unknown)	_____ had 18 fuzzy stickers. _____ had 6. How many fuzzy stickers do they have together?
SRU (Separate Result Unknown)	_____ had 16 cupcakes. He gave 7 of them to his friends. How many cupcakes does he have now?
MULT (Multiplication)	There are 9 muffins in a box. How many muffins are in 3 boxes?
PD (Partitive Division)	_____ has 12 cookies. He puts the cookies in 3 bags with the same number in each bag. How many cookies are in each bag?
MD (Measurement Division)	Ms. _____ bought 9 pencils. They are packed 3 pencils to a pack. How many packs of pencils did she buy?
CDU (Compare Difference Unknown)	_____ has 13 erasers. _____ has 8 erasers. How many more erasers does _____ have than _____?
PPW-PU (Part Part Whole - Part Unknown)	There are 21 sour candies in a jar. 8 are pink and the rest are green. How many green sour candies are in the jar?
JCU (Join Change Unknown)	_____ has 9 toys. How many more toys does she need to have 21 toys altogether?
SCU (Separate Change Unknown)	12 kids were at the playground. Some children went home. Now there are 4 kids left at the playground. How many children went home?
JSU (Join Start Unknown)	_____ has some books. He buys 6 more books at a yard sale. Now he has 11 books. How many books did he have before?
SSU (Separate Start Unknown)	There were cookies in a cookie jar. _____ took 7 of them. Now there are 15 left. How many cookies were in the jar to begin with?
CQU (Compare Quantity Unknown)	_____ has 4 crayons and _____ has 7 more than _____. How many crayons does _____ have?
CRU (Compare Reference Unknown)	A blue jar has 15 buttons. It has 4 more buttons than a red jar. How many buttons are in the red jar?

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Thinking about Getting Pregnant? Last Week to Register!

My Purposeful Conception: Preparing Your Mind, Body, and Life for Pregnancy e-course was dormant for a while as I figured out how to get back on my feet after giving birth to two children, building our dream house, and starting an organization and a school.

But then I got an e-mail from a reader asking if we could partner on the course to get it back out into the world. At the same time, I saw a conception book sitting on my colleague’s desk. It rekindled in me a strong passion for helping families intentionally prepare for conception. It is literally one of the biggest decisions we can make in life and yet our culture doesn’t support much intentional thought around preparing for conception.

I ended up partnering with Katey Zeh who is just amazing. She inspires me with the way she thinks about the world and acts in ways to make it better.

We are starting our next course on April 3. We would be so grateful if you could help us spread the word far and wide! If you can think of someone who might be interested, here’s a blurb you could copy, paste, and send to them:

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Hi! I thought you might be interested in this e-course called Purposeful Conception: Preparing Your Mind, Body, and Life for Pregnancy. It was created by the blogger behind Feeding the Soil. It starts on April 3. If you’re interested, you can read more about it here or register here. Have a great day!

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On Self-Compassion

A post shared by Matthew Bradford (@mattyrunrun) on Mar 17, 2017 at 8:07pm PDT

One of the things I'm working on with my leadership coach is the concept of self-compassion. She recommended this awesome website that has some explanations, meditations, and exercises. 

One of the exercises I wanted to do was write a letter to myself that I could read on a daily basis. When I wrote the letter, I realized there was a lot of focus on my accomplishments. That's not the point! I'm supposed to be celebrating who I am, not what I've done. 

At the bottom of the letter, I wrote some affirmations that I can read to myself each day:

I have a unique set of skills and strengths.

I am valuable to my family and to the world beyond.

I have made and continue to make a positive impact on countless lives.

Montessori For All has an important role to play in the world.

I have the courage, strength, and resilience I need to face difficulty.

I am committed to constant growth.

I have everything I need.

I’m everything I need to be.

I am loved and have immense love to give.

I'm going to write them on a framed photograph in my bathroom so that I am forced to come across them frequently! My hope is to read them to myself every day.

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JOIN US!: Registration is currently open for the next Purposeful Conception Course: Preparing Your Mind, Body, and Life for Pregnancy, which starts on April 3! Register now! We'd love to have you join us!

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Life Is Short: Mini-Retirements

We got back from Spring Break in San Diego last week, and I am already dreaming and scheming about more travel with my family. I feel like this time with them is so fleeting, and I love having adventures with them. 

My current theory is that the way we think about retirement is completely messed up. Why work your butt off until you're really old and then get your free time? When your body doesn't feel very good? And your children are grown? 

I would much rather work longer (my job brings immense meaning into my life) and punctuate my life with more trips--"mini retirements," if you will, while I'm younger and my children are still at home. 

So I found a free home exchange website. It was easy to create a profile. In fact, you earn points just for creating a profile (points you can use to stay at someone's house for free!). And then you earn even more points if you create a profile for your home. I earned about four free nights just for completing those two steps. There are homes available all over the country and world! 

I'll let you know as a more coherent plan forms in my mind...

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JOIN US!: Registration is currently open for the next Purposeful Conception Course: Preparing Your Mind, Body, and Life for Pregnancy, which starts on April 3! Register now! We'd love to have you join us!

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Facing the Food Insensitivities

A post shared by Matthew Bradford (@mattyrunrun) on Mar 6, 2017 at 3:17pm PST

I'm finally getting to a place where I think I can tackle all the food sensitivities around here. Between my three guys, we are trying to minimize gluten, dairy, eggs, soy, and citrus. 

I tried brainstorming different categories of food, with the idea that the categories would help me search for recipes. Here are the categories I came up with:

1. Rice and beans
2. Curry
3. Tostadas
4. Tacos
5. Enchiladas
6. Veggie burgers
7. Pasta
8. Chili
9. Sushi
10. Fried rice

So for this week, here are the five recipes we are going to try: 

• Rice & Beans: Braised Coconut Spinach and Chickpeas with Lemon
• Tostadas: Black bean with quick pickles and soft-cooked eggs
• Pasta: Creamy Avocado pasta
• Veggie Burgers: Quinoa and White Bean
• Curry: Golden Red Lentil Dal

Fortunately I'm feeling excited and optimistic about the challenge! I've been wanting to minimize gluten and dairy in my own life anyway. 

It definitely takes a lot of time to find recipes, but my hope is that we will build up a good reserve over time and it will get easier.

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JOIN US!: Registration is currently open for the next Purposeful Conception Course: Preparing Your Mind, Body, and Life for Pregnancy, which starts on April 3! Register now! We'd love to have you join us!

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Rage Against Uncomfortable Shoes

A post shared by Sara Cotner (@saracotner) on Mar 4, 2017 at 8:20pm PST

I find myself in a bit of a conundrum on a daily basis. I would be better at my job if I dressed more professionally. As an Executive Director of a non-profit organization, I have to raise a lot of money (millions), and I have to convince people that we can turn an ambitious vision into a reality. And whether I like it or not, my appearance is connected to my capacity to do that. I'm the girl who doesn't like to waste time or money with makeup. I only like comfortable shoes. And I don't like shopping. I don't want to waste time doing my hair every day. It's not a pretty combination. 

So when I find something that looks half-way professional and is comfortable, I'm ecstatic! Like these shoes I just got from Rothy's. They are made from recycled plastic and they are machine-washable. They are really comfortable (lots of padding for flats). So far, so good!

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JOIN US!: Register now for the next Purposeful Conception Course: Preparing Your Mind, Body, and Life for Pregnancy, which starts on April 3. There's still time to participate! Register now! We'd love to have you join us!

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Reflection & Rejuvenation: March

Two months down. Ten to go. It's strange to keep a pulse on the year and feel how quickly it passes. 

March! I'm excited for you. I have a 1.5-week break during March. More time with the boys. 

By the end of the year, I want to be able to say that I feel balanced, connected, full of vitality, and at peace. I want to keep my bucket full, so that I can interact with others from a place of patience, love, and joy. I'm still at about an 8 toward this goal right now! Not too shabby.

Here are the things I'm trying to do toward the above goal this year:

1. Run at least twice a week and do yoga at least once a week. Running = 80% of my goal this month. Not too shabby. Yoga = 0%. I'm having a hard time fitting this one in because of #4 (see below). I can't finish my work before I need to go to yoga, which would then necessitate working late into the evening, which I haven't wanted to do. 
2. Eat in a balanced and healthy way. Yes! This month wasn't as good as last month, but I did start eating salads for lunch, which is really exciting to me.  I need to recommit to not eating snacks at school. 
3. Continue my daily meditation and gratitude practice. I meditated 64% of the days in February (I use the Insight Timer app).
4. Stop working at 8pm to create two hours of free time for myself each evening. It's been more like 8:30pm this month, but I'm trying!
5. Attend therapy every other week and attend leadership coaching every other week. I took steps toward finding a therapist this month! 
6. Take a pottery class. Later in the year...
7. Host a Sunday Supper at least ten times this year. Yep! Hosted one in February and have already planned one for March.
8. Religiously use Mint.com to track our expenses. We have categorized all our expenses so far!
9. Restore our house each night. Better! 
10. Go on a retreat by myself. Later in the year...
11. Go on a trip with Matt. Later in the year...

Here's how I did on my February-specific goals:

• Getting our taxes done: Yes!
• Organize our office desk: Yes! I got these organizers from IKEA
• Organize the boys' bathroom (now that everything has a place in our house, I want to go back through one area per month to maintain it). Yes! 

Posting the goals on our giant kitchen whiteboard help keep them at the center of my mind. 

In March, I'll want to:

• Have an awesome Spring Break
• Schedule a dentist appointment
• Plan our summer (I'm traveling to Ohio for a four-week Montessori training)
• Organize the refrigerator side of the kitchen

And I wonder if we should knock out any of our Family Goals? Maybe go to the theater to see a production? 

I'm excited about what March has in store.

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JOIN US!: Registration is about to close for the next Purposeful Conception Course: Preparing Your Mind, Body, and Life for Pregnancy, which started yesterday! Register now! We'd love to have you join us!

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