Math teacher educator Pam Harris and her cohost Kim Montague answer the question: If not algorithms, then what? Join them for ~15-30 minutes every Tuesday as they cast their vision for mathematics education and give actionable items to help teachers teach math that is Figure-Out-Able. See www.MathisFigureOutAble.com for more great resources!
We've gotten a ton of questions about decimals. In this episode Pam and Kim discuss three different models and why they are great for questioning and building relationships, but may or may not be good for computation. Talking Points: Base Ten Materials Exploding Dots by James Tanton Money
Most students can scale up by ten as they begin to multiply larger numbers and that is a great starting place for students. In this episode Pam and Kim discuss a more sophisticated way of scaling numbers in multiplication problems. Talking Points: How beginning learners will use multiplying by 10 in double digit multiplication problems. How more sophisticated students deal with smaller numbers then scale up. How this applies to middle school students. How can Five is Half of 10 be used with more...
Often people misunderstand what this game we call mathematics is and feel they aren't good enough to play. In this episode Pam and Kim discuss how students need the opportunity to experience and play in the real game of mathematics. Talking Points: Mathematizing is not about speed Pam, the basketball player It's not about memorizing disconnected rules and procedures. Kim, the teacher pleaser Experience and opportunities are important so kids have choices We need all students in the game of math ...
It's our two year anniversary! We are so grateful you've spent this time with us. In this episode Pam and Kim discuss openly things they've learned and how they've grown during their journey as math teacher educators. Talking Points: It's not 'Pam Math', it's Real Math and developing mathematicians! Coaching teachers is about mentoring, not just telling The importance of a common vocabulary - Check out Episodes 58 and 101 Empowering teachers and leaders through Journey and Journey Leader Deep di...
What are some examples of rich tasks that are designed to intrigue and engage students? In this episode Pam and Kim give some specific examples and describe why they are so rich. Talking Points: Relatable to students not just real world An eye towards equity Lead to the mathematics Packed with patterns Natural extensions Make the math realizable Building Powerful Linear Functions coming Fall 2022 See Ep 47: Fractions as Fair Sharing where we explored the Sub Sandwich rich task!...
Let's talk rich tasks! On Twitter we enjoyed a great conversation about what makes a rich task rich. We thought we'd comment on some great suggestions from Professor Tad Watanabe, inspired from his mentor Dr. Grayson Weatley. Talking Points: Invite students to make decisions Replete with patterns Promote discussion and communication Tasks should lead somewhere Be extendable Have an Element of Surprise And More!
What comes to mind when someone says the word "strategy"? There are at least four different meanings for the word "strategy" in mathematics teaching. In this episode Pam and Kim parse out the different meanings and discuss how those meanings shape the outcomes of our teaching. Talking Points: Numeracy Strategies Problem Solving Strategies Teaching Strategies Strategies for Teaching Why without one type of strategy, the other strategies will fall flat...
We love that we've been able to make 100 episodes! We also love that 1 hundred is 10 tens, so let's talk place value! In this episode Pam and Kim discuss why students struggle with place value, and suggest some of their favorite place value activities. Talking Points: Why 'place labeling' is ok, but not enough Count Arounds Multiple Towers Base 10 materials Using correct place value language
In the last 5 episodes we've laid out the most important strategies for students to be able to solve for all four operations. So what? In this episode Pam and Kim solve a gnarly problem to demonstrate how mathematizing can empower you and your students, and open up to the world of Real Math. Talking Points: How to use the BIG downloadable e-book A gnarly problem solved using Real Math It's all about efficiency and developing more sophisticated reasoning Partial strategies are a great starting po...
Division is figure-out-able! In this episode Pam and Kim discuss the four main strategies students need to develop to solve any division problem that's reasonable to solve without a calculator. Talking Points: Pam's personal harmful experience from the long division algorithm A precursor strategy: Partial Quotients Smart Partial Quotients Over-Under 5 is Half of 10 Equivalent Ratios Combining strategies Get the BIG download of all the major strategies for addition, subtraction, multiplication, a...
What are the five major strategies for multiplication? In this episode Pam and Kim name and give examples of each of the five major multiplication strategies. If students own these strategies they should be able to solve any multiplication problem that is reasonable to solve without a calculator. They will be able to solve it as efficiently as a traditional algorithm and most of the time more efficiently than the traditional algorithm. But even more important than that, they will be developing M...
It's time for subtraction! In this episode Pam and Kim name and give examples of the four main subtraction strategies students need to own to solve any subtraction problem that is reasonable to solve without a calculator. Talking Points: Remove a Friendly Number Remove a Friendly Number - Over Remove to a Friendly Number Constant Difference How do students choose which one to use? Get the download! www.mathisfigureoutable.com/big...
What are the major strategies students need to know to solve any addition problem that is reasonable to solve without a calculator? In this episode Pam and Kim list them out, give examples, and some insights into how they choose which strategy to use for any given problem. Talking Points: Splitting by Place Value (a precursor strategy) Add a Friendly Number Add a Friendly Number - Over Get to a Friendly Number Give and Take When do you use each strategy? Get our download of all the major strateg...
We want students to be real problem solvers, and we know that means much more than helping them get correct answers. But we never want to put students in a position where they are disadvantaged because they don't know the traditional algorithms. We actually want them to have a much deeper and richer understanding of mathematical relationships. In this episode Pam and Kim begin a series exploring the major strategies for each operation that students need so that they can solve ANY problem that's ...
When we feel passionately about the way we teach, we can sometimes inadvertently miscommunicate when speaking with parents. In this episode, Pam and Kim discuss how to appropriately talk about getting correct answers and preparing for high stakes tests so that parents know their children are in good hands. Talking Points: Answers are important! What we don't want to communicate to parents Preparing students for high stakes tests is important! Insight into a test writer's thinking when they write...
Partnering with parents can be a blast! In this episode Pam and Kim describe how they organize and run math nights to help parents experience mathematizing and get excited about what their students will be learning. Talking Points: Typical parent math nights vs. our parent math nights Opportunity to share grade level or school wide expectations Importance of a Q & A for parents Help parents experience math the way their students do Mathematizing for parents at the "sweet spot" level of math ...
How can we proactively partner with and support parents? In this episode Pam and Kim discuss ways they over communicate to parents to keep parents involved and not confused. Talking Points: Newsletters: What is helpful information and tips for parents I can share? Parent-teacher conferences: What can I share with parents about math other than just grades? Homework assignments: I don't like drill and kill. What kinds of homework are helpful for students and parents?...
Parents are so important, and sometimes they get concerned when their child isn't being taught math they way they were expecting. In this episode Pam and Kim discuss hearing parents' concerns and helping them feel heard and then helping them understand the math. We appreciate parents and we are better with them! Talking Points: We want invested parents Parents need to be heard, and then they need to understand The importance of listening to understand...
Kim has a story to tell that Pam hasn't heard yet! Listen in to get a feel of how math can be when students understand that Math is Figure-Out-Able. Talking Points: Pajama Math and exploring relationships in multiplying fractions Can you really just multiply straight across with fractions? Two ways to reason about 3/5 times 3/9 Pam and Kim reason multiple ways about 3/4 times 2/5 Join us in #MathStratChat!
Most of us are probably teaching the way we were taught, to get correct answers to problems. But we aren't actually helping students understand and reason about the math. Which is more important? In this episode Pam and Kim discuss answer getting versus relationship building. Talking Points: Phil Daro's research on patterns of math instruction from across the world Student success from answer getting instruction vs instruction that focuses on outcomes from reasoning The real purpose of math clas...
Do your standards require you to teach algorithms? What then? In this episode Pam and Kim discuss how they prepare their students for success on high stakes tests without ever teaching a step by step algorithm or process. Talking Points: All year long invest your time wisely helping kids learn to reason, increasing their sophistication of relationships and solving more difficult problems. Students can and will perform well on standardized tests if they have been thinking and reasoning, experienc...
What purpose has and should algorithms have in mathematics education? Are step by step What purpose has and should algorithms have in mathematics education? Are step by step procedures even to be taught at all? In this episode Pam and Kim talk about our role as teachers and what students need to think like mathematicians. Talking Points: One student's perspective What are algorithms? Why have we taught algorithms in the past? Where are algorithms helpful in today's world? Do algorithms help stud...
Aren't addition facts cool?! By this point you've learned some amazing relationships and strategies to help your students make real sense of and automatize the single digit addition facts. But sometimes learning and applying are two different things. In this episode Pam and Kim detail how to help your students get out of counting mode and actually apply the relationships they've learned to become fluent with single digit addition facts. Talking Points: Why do some kids keep counting after they'v...
It's time for you to learn about the most important relationship your students need to know to automatize their addition facts: partners of ten. Partners of ten influence strategies for adding bigger numbers as well as strategies for other operations. In this episode Pam and Kim will discuss some of those influences and some games and routines specifically made to provide experience and build partner of ten relationships for all levels and all ages. Talking Points: What are partners of ten? Do o...
We build addition facts through relationships and fluency through experience. So what important patterns and relationships can help students master or reason with their single digit addition facts rather than rote memorize? How can we teach those patterns and what experiences can help students automatize and become more fluent with addition facts? In this episode Pam and Kim dig deeper into single addition facts and how we as teachers can can empower students to reason like mathematicians. Talki...
Addition is figure-out-able! In this episode Pam and Kim describe some of the fundamental patterns students should learn as they get familiar and automatize with their single -addition facts. We want students at all levels to have access to their facts so they don't bog down every time they encounter them. Talking Points Connecting the concrete and pictorial experiences to symbolic representation. Tips for using flash cards and addition table. Noticing patterns can reduce the number of addition ...
So many people get left behind when it comes to higher math, because they never learned mathematize or to think more sophisticatedly and build complex relationships and simultaneity in lower math. Teachers often share that their students lack numbers sense or fluency, specifically lack of memorized basic math facts. That's why in this episode Pam and Kim start a new series on single digit addition fact fluency. Are the facts important? You bet! But how they are taught is even more important to b...
We've come to the end of another year, and we'd thought we'd leave you with some suggestions on goals you can set for your teaching. In this episode Pam and Kim highlight some transformative goals that you probably haven't considered before. How could your math class look next year or next semester? Talking Points: Learners setting goals around mathematical behaviors or practice standards. Teacher goals centered around the NCTM mathematics teaching practices. Teacher goal to elicit and use evide...
Don't you love the holidays? We sure do! It's such a great excuse to talk math with your family! In this episode Pam and Kim describe some ways (and activities they do) to involve math in their festivities, from formal games like I Have, You Need, Guess My Number, MathStratChat, to simply noticing and wondering. Talking Points: Cooking and Baking Spending Holiday Money Dinner Games Daily Tasks Walks Car Games Notice and Wonder...
As we approach Christmas and the holidays, we thought we'd talk about some of our favorite games that we love to gift others! In this episode Pam and Kim share what makes a great mathy game and list a few of their favorites that not only have numbers, but include some with strategy and logic. Also, don't forget to check out some of our Math is Figure-Out-Able merch for your own gift list! Favorite Games: Splendor Multi (by joyfulmathematics.com) Prime Climb (by mathforlove.com) Tiny Polka Dot (b...
