Summer—a time for refreshment, for renewal. And for many of us, for review.
I don’t know about your children, but I have found that my daughter quickly loses math skills, speed, and insights if they are left to lie dormant for an entire summer. And sometimes we just don’t make as much progress on mastering key concepts during the regular school year as we would have liked. Yet, I like to come back to our primary math curriculum with fresh interest in the fall, so I prefer to set it aside between school years. This means I am always looking for resources to get us thinking about and experiencing math in new ways. I would love to share with you some of the key resources and ideas that have helped our summers of review leave us feeling rested, refreshed, and eager to try our hand at our primary math curriculum come fall.
We focus on several key areas. First, I like to expand our mathematical horizons by exploring ideas that might not be included in the usual scope and sequence. I want us to be excited about math, intrigued by math, challenged by math. This provides the twin benefits of both a larger vision for mathematics and a willingness to dive back into our little corner of math again—whether that means simply increasing speed and accuracy with basic skills and operations or mastering key concepts so that we are ready to wield them efficiently the following year. Where possible, I like to give my daughter a gentle, conversational introduction to any new big ideas I know she will encounter during the fall so that they are not brand new and completely intimidating. I also like to challenge her to develop stamina and patience with math through thought-provoking problems or puzzles. It takes a special kind of mental perseverance to sustain focus on a tough, multi-faceted problem, and we use the summer to build these mental muscles.
We take full advantage of the slew of fascinating children’s books on mathematical concepts at our library. We spend a lot of time at the library in the summer, and with each visit, we make sure we check out one or two of these math books each time we stop by. We have explored mathematical ideas through beautifully illustrated books like “Infinity and Me” and “Growing Patterns: Fibonacci Numbers in Nature,” and honed our problem solving skills through stories like “Anno’s Magic Seeds” and “Panda Math.” Each new book is a fresh adventure with a unique perspective on math. They leave us feeling energized, and they often inspire mathematical conversations outside of “math time.”
Just like science, mathematics developed within history and in response to specific intellectual movements and practical needs. For math to really make sense to us, it needs to live within its context in history. We have enjoyed watching the excellent lecture series titled Queen of the Sciences: A History of Mathematics from the Teaching Company (see if your library has it!). Of course, the advanced mathematics in the latter lectures is well above my daughter’s abilities (and sometimes mine!), but the grounding in the history of mathematics was invaluable, and we look forward to watching the series again in future summers and gleaning more from it each time as our knowledge develops. We absolutely love the gorgeous book with the deceptively simple title, The Math Book. As its subtitle explains, it offers brief, one-page summaries of 250 milestones in mathematics “From Pythagoras to the 57th Dimension.” This is a coffee table math book with stunning photographs illustrating and illuminating each milestone. This is a book that exposes readers to ideas they have never considered and fields of mathematics they have never heard of, and invites them to dig deeper.
These resources leave me, as the math teacher, inspired to engage with mathematics in new ways and they add depth and breadth to my mathematical knowledge in a truly enjoyable format. My daughter enjoys them as well, but often these are primarily equipping and refreshing for me—the math teacher. I have also appreciated the Cultivating Classical Parents webinars available on CC Connected covering topics like “The History of Number,” “Using Examples to Teach Math,” and “Using the Five Common Topics to Teach Math” as other ways to expand my horizons and prepare me to better lead mathematical conversations with my daughter.
Speed and Accuracy
Math games allow us to actively build relationship even as we drill speed and accuracy with basic math facts and operations. We relish time spent together on math games and puzzles; many weeks I ask my daughter to select a math game per day that she would like to play with me. We enjoy card games like those found in the Classical Conversations Quick Flip Arithmetic Book and dice games like the fast-paced and exciting Slam Game, a longtime family favorite. Playing a round or two of board slam is always fun, and it actually sometimes even happens on the weekend with Dad! (And it comes with the added incentive of possibly being prepared to compete in National Number Knockout someday.) All of these games drill basic operations and skills, provide continual review of math facts, and help increase speed and accuracy of computation—skills that we are so grateful for when we resume our regular math routine.
We also love to read through the delightful Bedtime Math series together as a way to make sure we can apply our speed and accuracy to specific situations. Each of the four books in the series presents brief and often funny one- or two-paragraph scenarios, and then asks several word problem questions based on the scenario. This is a fabulous resource for one-room-schoolhouse math as the questions based on each story become increasingly difficult. The first question for each scenario is labeled “For Wee Ones,” the second for “Little Kids,” the third for “Big Kids,” and the last is a “Bonus” question. Although we had only one child when we first started using the books, they were still a great resource. The confidence my daughter gained from correctly interpreting the information presented in the scenario and accurately answering the simpler questions gave her the courage to tackle the bonus questions, whereas if we had gone straight to the bonus question, she would have felt intimidated and overwhelmed. And even if she occasionally needed help with the bonus question, it didn’t strike the same blow to her problem-solving confidence since she was able to correctly answer the first three questions.
Sometimes my daughter just needs a fresh take on a concept that has been eluding her. For this, we will often try out Khan Academy’s videos and accompanying online practice problems for a change of pace. Sal’s simple and straightforward explanations are always helpful, and at times the gamification of the practice problems is just the motivation my daughter needs to press forward even when the going is tough. We have also found that we can depend on the Life of Fred series to explain concepts in a new way. We love this series with its quirky story-telling about the five-year-professor Fred Gauss (who read a lot when he was a baby) and its engaging way of continuing the story through the practice problems at the end of each chapter billed as “Your Turn to Play.”
If we just need lots of practice, the “Key to…” workbook series published by McGraw Hill has proven very helpful. It provides copious practice problems narrowly focused on a specific concept with very gently increasing difficulty levels. Each major topic such as decimals, fractions, percents, algebra, and geometry is covered in several slim volumes. Each individual volume does not take long to complete—my daughter will usually knock one out in a week or two—which can be a very satisfying way for her to tangibly experience the progress taking place.
Patience and Persistence
We will always be grateful that we stumbled across KenKen puzzles—free, printable puzzles available online that drill basic math skills in an engaging and challenging way while also requiring logic and developing perseverance and mathematical stamina. These qualities shine during the fall when we are tackling new and difficult concepts, and my daughter is able to sustain her focus and patience even when something doesn’t come easily to her. The puzzles are customizable for different skill levels, so this option is another great choice for one-room-schoolhouse summer math.
One summer I decided to organize a math circle for my daughter and any interested friends that wanted to join us. One of the many things I loved about the math circle was getting to challenge students to be willing to engage in sustained mathematical thought—something that their daily math didn’t require of them but a skill they would need as they entered the dialectic years. Each week I would hand out a Problem of the Week sheet with a challenging problem and this reminder printed at the bottom of the paper: “Remember! The Problem of the Week is meant to be tricky. You may or may not be able to solve it in one week. Write down any thoughts you have, any ideas you wonder about, or any questions you might want to consider as you try to solve it. Bring everything you wrote to the next class.” I would ask questions involving number patterns and functions, or pose logic puzzles pulled from a variety of sources. At the beginning, the students would often groan upon reading the problem and decide it was unsolvable. But most would come back the following week with the problem solved or some excellent questions that would allow us to solve it together as a group. By the end of the summer, I could ask much more complex questions confident that they would have the stamina and sustained interest to work out the answer. Whether or not you start a math circle, selecting a Problem of the Week during the summer can be a fun way to develop your child’s mathematical stamina.
Problems posed in books like Professor Stuart’s Cabinet of Mathematical Curiosities can sometimes occupy our summer afternoons, and they certainly challenge us to stretch our mathematical muscles. We have enjoyed projects from The I Hate Mathematics! Book like one that involves sidewalks and chalk and invites students to think about patterns, and others that inspire students to compose and solve mathematical problems in their daily lives. My daughter pores over the Childcraft Mathemagic book with its logic puzzles, word problems, histories of number systems from around the world, excerpts from great math-related stories, and so much more.
Of course, I have only scratched the surface of the amazing resources available to help both students and teachers prepare for a new school year of math. But I hope I have been able to start an ongoing conversation about how math can fit into the three Rs of summer—refreshment, renewal, and review.
How do you work to expand your own mathematical horizons? What are your favorite methods to drill speed and accuracy? Do you have a favorite way to tackle new concepts? How do you challenge your students to develop their mathematical patience and stamina? Do you have any math resources that leave you feeling refreshed and renewed? Please use the comments to share some of your favorite ways to enjoy math together!