TNL offers six different Thought Exercises to prompt authentic math learning. As their categorization implies, TE's are more than mere routines. They create a know-building community that enhances learning skills and reinforces conceptual understanding: drive.google.com/file/d/1XCS3...
When learners are expected to look for relationships between numbers, facts have real meaning.
When we embrace the idea of teacher as facilitator of math learning, we view mathematics and teaching as creative pursuits.
Discourse-rich classrooms offer learners excellent opportunity for deep learning as well as the enhancement of crucial learning skills. And because critical discourse allows learners' thinking to be highly visible, teachers are able to assess learning and offer feedback in realtime.
#iTeachmath
So, how do we convince the masses of the necessity of replacing a public school system that was solely developed for the preparation of labor for one concerned with maintaining a highly informed, critical thinking, positive change affecting, humanity-centered citizenry?"
Here are three ideas for feedback:
(1) Discuss the way in which the learner expressed equality; 1/2 does not equal 3.5/3
(2) Introduce the concept of complex fractions
(3) Express 3.5/3 multiplicatively, 3.5(1/3) or (3 1/2)(1/3), and apply the distributive property: 3(1/3) + 1/2(1/3) = 1 1/6
" If we encourage teachers to be more confident in their own math abilities the next generation will have stronger skills and greater confidence in math...Both students and teachers must understand how math works at the conceptual level...'The conceptual part is, why does that work?' " #iTeachmath
Yes! Deep understanding...isn't that the goal?
#iteachmath #edusky #ElemMathChat #mtbos
Learning is messy. It requires taking risks to make connections, formulate conjectures, and refute others' assertions.
Yes! This is an excellent way for learners to assess and enhance crucial learning skills.
Indeed: "The magic truly happens when mathematicians make sense of and solve problems together."
#iTeach #iTeachMath #mathmagician #ElemMathChat
Yes. When young learners are introduced to a strategy that is presented as "the way" to approach a particular kind of problem, why should they have to give any thought to this kind of problem when they encounter it again in the future? Their thinking is impeded.
Yes: "...But I teach so they can know the math well enough to score well (not 'test prep')."
Truth. And this is the reason that math PD has to be concerned with mathematics itself, not merely the implementation of a program/curriculum. Teachers can implement with greater fidelity when they are able to identify and make connections between mathematical ideas for themselves.
Yes. Real math pd is about the mathematics itself, not merely the math program/curriculum.
Yes. Excellent point.
Learners would have the opportunity to make sense of expressions and equations by identifying underlining mathematical ideas. A lesson on "how to" simplify complex expressions becomes conceptualizing addition through a discussion of units and an analysis of terms.
drive.google.com/file/d/1mPRK...
Indeed. Learning is more powerful when it happens in community.
Yes! Meaning-making and sense-making are essentially human tasks. Storing, sorting, and organizing information are essentially technological tasks (one we've designed tools precisely for!). Our brains can certainly do both, but the reason we offload the latter is to facilitate the former.
When teachers are given the opportunity to have richer, more authentic learning experiences with the math they are expected to teach, their learners can have richer, more authentic learning experiences with the math they are expected to learn.
#EduSky #MTBos #MathSky #iTeachMath
Let's work to improve math learning by helping teachers to experience more effective professional learning: content-focused for deep conceptual understanding, highly collaborative, and learning skills enhancing.
#EduSky #MTBos #MathSky #iTeachMath
Indeed.
The teacher is expected to do all of the thinking.
"This might be the most fundamental aspect of constructivist classrooms: adults modeling for children that learning is not merely a schoolhouse collection of correct answers but that the world itself is full of complex problems w/ multiple perspectives...that merit our thoughtful consideration..."
"In our work, we’re also looking at “power skills” -- skills that power the learning process. Knowing fractions is important, but believing you’re a math learner is equally as powerful."
T. Lovelace
www.edsurge.com/news/2024-11...
"We often ask learners to pause learning to be assessed. Ideally, we should think about how to assess them while they continue learning, whether individually, in groups or in their community." - Temple Lovelace
Yes, math learning should be a journey in which there is time to get stuck...to ponder...to question...to struggle all for the purpose of developing deep, conceptual understanding of mathematical ideas.
