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What perspective and assumptions do you bring to your teaching? In this episode, Pam and Kim introduce a model mapping teaching style (direct teach vs. inquiry) against whether a teacher "maths" (uses relationships/connections) or mimics/rote memorizes. Talking Points: "Inquiry-based" + Mimicking"Direct teach" + Mimicking"Inquiry-based"+ Math-ing"Direct teach" + Math-ingLinks: 1. REGISTER for FREE 6-8 Book Launch Webinar  2. BLOG: When "Covered" Doesn't Mean Understood: Building Reasoning in Middle School Math 3. Developing Mathematical Reasoning Book Series Check out Pam's social media Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Linkedin: Pam Harris Consulting LLC

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 7, 2026.  Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.  Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education

What can we do to keep students thinking, instead of waiting to be told what to do? In this episode Pam and Kim focus on an algebra Problem String that helps students learn to choose between strategies. Talking Points: What it mean to keep kids in "Thinking Land"How to keep students actively reasoning versus cueing them to mimic/memorize stepsHow the same instructional phrase can lead students into or out of "Thinking Land"Ask yourself: "Is this direct move keeping kids reasoning, or just cueing mimicry?"Links: 1. REGISTER for FREE 6-8 Book Launch Webinar  2. BLOG: When "Covered" Doesn't Mean Understood: Building Reasoning in Middle School Math 3. Developing Mathematical Reasoning Book Series Check out Pam's social media Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Linkedin: Pam Harris Consulting LLC

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 30, 2026.  Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.  Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education

What does explicit teaching mean to you? In this episode, Pam and Kim discuss an Adding Mixed Numbers Problem String, idenitfying exactly what teachers should be explicit about versus what they should leave for students to grapple with. Talking Points: Being explicit about the student's job during a Problem StringWays to nudge students to make connectionsEliciting specific strategiesCreating helper problems Links: 1. Register for 6-8 Book Launch Webinar 2. Pam's Books 3. Math is FigureOutAble Blog Check out Pam's social media Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Linkedin: Pam Harris Consulting LLC

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 23, 2026.  Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.  Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education

When do we allow students more freedom, and when do we need to be more explicit? In this episode, Pam and Kim analyze a Distance vs. Removal subtraction Problem String, identifying when they are explicit and when they are not. Talking Points: Intentional contexts, number choices, and problem orderChoosing which strategies to elicit and representPlanned board layouts Focusing the conversation Highlighting mathematical behaviorsLayering explicit content, behavior, and community goals around open-ended student reasoningLinks: 1. Podcasts Episodes Distance vs. Removal: Ep96 and Ep149  2. Pam's Books Check out Pam's social media Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Linkedin: Pam Harris Consulting LLC

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 16, 2026.  Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.  Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education

Many aspects of teaching can be improved by being more explicit. In this episode, Pam and Kim identify specific categories where explicit teaching is necessary, borrowing Piaget's distinction between social-conventional and logical-mathematical knowledge. Talking Points: Being explicit about a goal doesn't mean teaching it as a step-by-step procedure.Good teaching requires explicit goals.Examples of Math Content Goals Examples of Math Behavior Goals Examples of Community Behavior Goals Links: FREE DMR Registration LinkMath is Figureoutable BlogPam's BooksCheck out Pam's social media Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Linkedin: Pam Harris Consulting LLC

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 9, 2026.  Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.  Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education

Is the popular discussion around "explicit teaching" helpful? Do we all envision the same thing? In this episode, Pam and Kim discuss their thoughts about "explicit teaching", and which parts of mathematics require explicit teaching, and which do not. Talking Points: The difference between social-conventional knowledge and logical- mathematical knowledgeExamples of social knowledge and when students must be told something in mathematicsExamples of logical-mathematical knowledge and how it should be built through experiences, not rote rules.Most of mathematics is logical-mathematical and requires varied experiences.Links: FREE DMR Registration LinkMath is Figureoutable BlogPam's BooksCheck out Pam's social media Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Linkedin: Pam Harris Consulting LLC

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 2, 2026.  Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.  Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education

What does reasoning about algebraic expressions look like? In this episode, Kim facilitates a Problem String that has Pam solving equations using equivalence. Talking Points: Using comparison to ignore commonalities on both sides of an equationEquivalence strategies are the most sophisticatedLearning to think relationally, rather than procedurallyRelational thinking builds mathematical identity and genuine engagementLinks: FREE DMR Registration LinkMath is Figureoutable BlogPam's BooksCheck out Pam's social media Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Linkedin: Pam Harris Consulting LLC

In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 26, 2026.  Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.  Check out #MathStratChat on your favorite social media site and join in the conversation. Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education

With so much to teach every year, we know you're always looking for the biggest impact for long term success for your students. In this episode, Pam and Kim discuss models that grow with students as they learn more and more mathematics. Talking Points: Verticality in practice standards, content progressions, vocabulary, notation, and strategies How area models extend from elementary to high schoolOpen number lines mature into double number linesRatio tables can start as early as 3rd grade and scale to decimals, large numbers, proportional relationships.How models act as lasting mental anchors, not just "picture drawing" as a substitute for mathematical ability.Links: FREE DMR Registration LinkMath is Figureoutable BlogPam's Books Check out Pam's social media Twitter: @PWHarris Instagram: Pam Harris_math Facebook: Pam Harris, author, mathematics education Linkedin: Pam Harris Consulting LLC