sense
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.
The language that children bring with them to school involves a broad set of skills rooted in the early context of adult-child interactions.
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.
Would the mother’s learning of formal mathematics be enhanced if it were connected to this knowledge? The literature on learning and transfer suggests that this is an important question to pursue.
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.
They found that students learned subsequent text editors more rapidly and that the number of procedural elements shared by two text editors predicted the amount of this transfer. In fact, there was large transfer across editors that were very different in
This is what we hope to achieve in our dual-immersion program with children making quick connection in their non-native language.
Research has indicated that transfer across contexts is especially difficult when a subject is taught only in a single context rather than in multiple contexts
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.
Motivation affects the amount of time that people are willing to devote to learning.
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.
students need feedback about the degree to which they know when, where, and how to use the knowledge they are learning.
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?
Attempts to cover too many topics too quickly may hinder learning and subsequent transfer
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.
Transfer is affected by the degree to which people learn with understanding rather than merely memorize sets of facts or follow a fixed set of procedures; see Boxes 3.3 and 3.4.
What we learn with pleasure, we never forget!
For example, young children often erroneously believe that they can remember information and hence fail to use effective strategies, such as rehearsal.
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.)
Steven began his unit on Hamlet without ever mentioning the name of the play. To help his students grasp the initial outline of the themes and issues of the play, he asked them to imagine that their parents had recently divorced and that their mothers had taken up with a new man. This new man had replaced their father at work, and “there’s some talk that he had something to do with the ousting of your dad” (Grossman, 1990:24). Steven then asked students to think about the circumstances that might drive them so mad that they would contemplate murdering another human being. Only then, after students had contemplated these issues and done some writing on them, did Steven introduce the play they would be reading.
Building student interest in a topic
In fact, expertise can sometimes hurt teaching because many experts forget what is easy and what is difficult for students.
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.
One way to help students learn about conditions of applicability is to assign word problems that require students to use appropriate concepts and formulas (Lesgold, 1984, 1988; Simon, 1980). If well designed, these problems can help students learn when, where, and why to use the knowledge they are learning. Sometimes, however, students can solve sets of practice problems but fail to conditionalize their knowledge because they know which chapter the problems came from and so automatically use this information to decide which concepts and formulas are relevant. Practice problems that are organized into very structured worksheets can also cause this problem. Sometimes students who have done well on such assignments—and believe that they are learning—are unpleasantly surprised when they take tests in which problems from the entire course are randomly presented so there are no clues about where they appeared in a text (Bransford, 1979).
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!
The historians excelled in the elaborateness of understandings they developed in their ability to pose alternative explanations for events and in their use of corroborating evidence. This depth of understanding was as true for the Asian specialists and the medievalists as it was for the Americanists.
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.
Within this picture of expertise, “knowing more” means having more conceptual chunks in memory, more relations or features defining each chunk, more interrelations among the chunks, and efficient methods for retrieving related chunks and procedures for applying these informational units in problem-solving contexts
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.
xperts’ thinking seems to be organized around big ideas in physics, such as Newton’s second law and how it would apply, while novices tend to Page 38 Share Cite Suggested Citation:"2 How Experts Differ from Novices." National Research Council. 2000. How People Learn: Brain, Mind, Experience, and School: Expanded Edition. Washington, DC: The National Academies Press. doi: 10.17226/9853. × Save Cancel perceive problem solving in physics as memorizing, recalling, and manipulating equations to get answers.
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.
For example, electronics technicians were able to reproduce large portions of complex circuit diagrams after only a few seconds of viewing; novices could not.
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.
Chess masters perceive chunks of meaningful information, which affects their memory for what they see. Chess masters are able to chunk together several chess pieces in a configuration that is governed by some strategic component of the game.
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.
Are not community centered
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.
students might help one another solve problems by building on each other’s knowledge, asking questions to clarify explanations, and suggesting avenues that would move the group toward its goal
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.
a teacher constructs an instructional program
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.
Teachers must come to teaching with the experience of in-depth study of the subject area themselves.
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.
For the scientific understanding to replace the naïve understanding, students must reveal the latter and have the opportunity to see where it falls short.
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.
A logical extension of the view that new knowledge must be constructed from existing knowledge is that teachers need to pay attention to the incomplete understandings, the false beliefs, and the naive renditions of concepts that learners bring with them to a given subject.
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.
rather, the goal of education is better conceived as helping students develop the intellectual tools and learning strategies needed to acquire the knowledge that allows people to think productively about history, science and technology, social phenomena, mathematics, and the arts.
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.
Developmental researchers have shown that young children understand a great deal about basic principles of biology and physical causality, about number, narrative, and personal intent, and that these capabilities make it possible to create innovative curricula that introduce important concepts for advanced reasoning at early ages.
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.