Some of this comes from lack of experience with word problems, but some will be the natural product of teaching strategies. I have seen teachers focus heavily on building charts of words and which mathematical operation they relate to in an attempt to prepare for standardized tests. While a temporary fix, it doesn't do much for understanding the intent of the problem.

Building vocabulary is one of the topics that keeps coming up in these chapters. A precise vocabulary is what enables children to categorize concepts more specifically and make connections. If you don't have a word for an item, you can't connect to it.

For example, there are words I know in Chinese that I do not have language for in English. I can connect those to concepts in Chinese, but my vocabulary is not precise enough to expand it across languages.

At this point, would there be a need for formal knowledge of mathematics? Isn't the goal of education to prepare a person to be a successful, contributing member of society? She seems to have accomplished that independently through experience.

This is what we hope to achieve in our dual-immersion program with children making quick connection in their non-native language.

I've seen this in our dual-immersion program as children begin to understand the nuances of each language and make connections to concepts they learned in the other language.

Don't even dare try to get a PreK student to do something that doesn't interest them!

As teachers, we can chose how to present various objectives. Teaching material within themes that interest students keeps them engaged, which leads to better retention of content.

What does feedback look like in the early years? Perhaps the ongoing dialogue that happens in pretend play or naturally occurs in open-ended questions?

Often, we are pacing our lessons too quickly to give children meaningful opportunities to engage with concepts. Working with PreK and K students, we often have to stop and remember that this is their first school experience and that time spent exploring new situations and materials provides the context to apply future knowledge to. Rushing is a disservice to their future education.

What we learn with pleasure, we never forget!

Where would their understanding of what it means to be prepared come from? If teachers don't teach readiness, we can't expect students to be truly ready themselves.

Checklists help with this: I am ready when I.... have completed a poster that includes words and photos. … have presented to a friend 3 times... etc.

Teachers can also model what preparation means by: verbally articulating that they are ready because their materials are gathered, sufficient, functional, etc. Likewise, they can identify the reasons why they are unprepared (didn't think carefully, the copier broke, etc.)

Building student interest in a topic

I spend a lot of time emphasizing this with our Nursery-Kindergarten teachers. When they are frustrated that children aren't sitting still on the carpet for their 20 min group time, we have to stop and remember that these children have never been expected to do this before. We can stop what isn't working and try something different (limit to 10 min, work in small groups, teach in another way, etc.). It also helps to reflect on what other skills are necessary before the current skill can be learned- before a child can sit in a group, he has to have core strength to hold his body upright.

This is one of the reasons we as a school are using a digital assessment tool which allows teachers to video students engaged in a real-world application, reflect on it, discuss it with the student later, or identify gaps in knowledge to readdress later.

I was that student who could tell you which page of the textbook the problem came from and thus how to solve it!

An interesting follow-up to this would be to know if these historians were able to answer factual questions in their youth and this understanding led to higher order thinking or do they have higher order thinking skills independent to the factual knowledge.

All of this is the product of many interactions with the content, trial and error, reading, experimenting, making mistakes and reflecting; it also comes from building a rich vocabulary in the subject matter.

Part of this has to be a lack of breadth of vocabulary in the subject matter. Nearest I can tell from this paragraph, both experts and competent beginners were able to reach accurate conclusions, but the articulation varied.

Experts have spent so many hours with content that content is chunked in complex ways which would cross all senses. I imagine an expert technician would have gained knowledge through listening, reading, experimenting, failing, reflecting, repeating... A novice may not have put in the time to apply content in all possible ways.

Chunking content into categories is critical for memory, but I also think that it is important to fit content into multiple categories to allow the content to be accessed from may different angles.

This is one area we have accidentally done well. As a small dual-immersion international school we don't have access to many resources that match our model well or are accessible in both languages. Instead, most of our PD is done by teachers. Our teachers appreciate learning new strategies from others in the same teaching environment.

I predict that in the future, we see a shift from individual knowledge to community knowledge, that is, the ability of a small group to harness their funds of knowledge, apply it to a problem, and test a hypothesis as a group. It will be less about who knows most and more about who knows which people know what concepts best and organizing those individuals to test a hypothesis.

I think it is important that teachers retain the role of constructing an instructional program and utilize the strengths and interests of the children when doing so. As was pointed out above, children learn best when they are able to use their preconceptions and misconceptions to test out new information. It is up to the teacher to know what her students know and harness this knowledge as a foundation for new concepts.

YES! There is a lack of truly knowledgeable teachers, especially in the early years and elementary. I work directly with 2-6 year olds who ask tons of questions. The main science focus in this age group is focused on plants and life cycles. I have observed so many wasted moments in the classroom because a teacher didn't know the answer to "how does the water go up the roots?" or "why are leaves green?" Teachers with rich background knowledge are able to apply that to the question and development of the child and continue to build layers of knowledge that will be added to in years ahead.

To do this, a school must value student-driven learning. Not many are willing to devote time to taking a child's idea, putting it to the test, and seeking additional information on the topic unless it is one that relates directly and specifically to the prescribed curriculum.

This comes about through dialogue with the child one-on-one or in a small group setting which is hard to find in modern class settings and teacher/student ratios. Young children who are given the opportunity to explore a rich environment and ask spontaneous questions are developing habits which will encourage them to keep learning through the rest of life.

I agree with this, but I am interested to see if this is seen as a negative or positive as the book continues. Personally, I think that this shift was viewed as a negative, isolating people from each other and building a dependency on AI up until a few years ago. At the moment, I see this view shifting to one of collaboration. I recently watched our elementary students preparing for a reading competition. They had 8 books for the team of 4. Amongst themselves, they decided to each read all the books, but then each took 2 books to read multiple times and be the "expert" on. I think dividing knowledge among people is becoming more important and it is becoming more acceptable to have depth of knowledge rather than breadth.

I have seen this first-hand with my preschoolers. It all starts when an adult takes the time to question a child about his/her thinking and understand what the child has observed or experienced that has influenced this thinking. I work in a bilingual Mandarin/English school and recently had quite a scientific conversation with a child who was telling me that the word for muscle and chicken are nearly the same in Chinese and that the chicken's muscles were the part we were eating for lunch.