20 Matching Annotations
1. Jun 2016
1. There are many appealing strengths to the idea that learning should be organized around authentic problems and projects that are frequently encountered in nonschool settings: in John Dewey’s vision, “School should be less about preparation for life and more like life itself.”

I agree and attempt to incorporate "real life" problems as often as I can into my classroom. The problem I often come across is the textbook's idea of a "real life" problem is often much different from what the students relate with. Still, it always helps to add context, especially in math where the question "where are we ever going to use this?" is asked on a daily basis.

2. there is an infinite number of numbers between any two rational numbers

This is a fact that can be really unsettling for students to hear, but is also very important for them to actually think about. It not only helps them understand fractions, but also the concept of infinity. Many students, even in high school just simply do not understand fractions, or are not willing to spend the time to complete problems with fractions.

3. Gradually, students come to ask self-regulatory questions themselves as the teacher fades out. At the end of each of the problem-solving sessions, students and teacher alternate in characterizing major themes by analyzing what they did and why. The recapitulations highlight the generalizable features of the critical decisions and actions and focus on strategic levels rather than on the specific solutions

This is challenging for me to get the hang of as a teacher. It is very easy for a class to do an activity, a then have the discussion get taken over by a only a few select students that were faster at catching on to the concepts. You really have to be careful as the teacher to make sure you allow for enough time so that all students are able to finish and form ideas about what they just learned. Then having a system to allow all groups to share something is very helpful.

4. Tests of transfer that use graduated prompting provide more fine-grained analysis of learning and its effects on transfer than simple one-shot assessments of whether or not transfer occurs

I like to use this type of graduated prompting when doing discovery based tasks. It allows me to give the appearance of giving students hints, when really I am just trying to get them to remember or realize what they already know.

5. For example, a group of Orange County homemakers did very well at making supermarket best-buy calculations despite doing poorly on equivalent school-like paper-and-pencil mathematics problems (Lave, 1988). Similarly, some Brazilian street children could perform mathematics when making sales in the street but were unable to answer similar problems presented in a school contex

This could come back to the idea that students perceive themselves as "bad at math" so in a school setting, they automatically shut down and don't actually think about the problems. But when they are presented outside of an educational context, they don't think about it as math, they just think about it as part of their job or social obligation.

6. e.g., a person may be performance oriented in mathematics but learning oriented in science and social studies or vice versa).

I come across this issue often in math classes. I have to be very careful when assigning tasks to students, because it is a very fine line between too easy and too challenging. Especially in math, it seems that there a lot of students who have just accepted that they are "bad at math" so they are quick to give up until someone explicitly shows them the answer and how to do it. This is a big issue that I try to fix with students on a daily basis.

7. A number of studies converge on the conclusion that transfer is enhanced by helping students see potential transfer implications of what they are learning

I also like to assign problems where students have to identify the error in another student's work. It seems to help students see common mistakes, and helps prevent them from making them in the future.

8. Understanding when, where, and why to use new knowledge can be enhanced through the use of “contrasting cases,” a concept from the field of perceptual learning (see, e.g., Gagné and Gibson, 1947; Garner, 1974; Gibson and Gibson, 1955). Appropriately arranged contrasts can help people notice new features that previously escaped their attention and learn which features are relevant or irrelevant to a particular concept

I like using this in situations where a short-cut may be able to be used for one math problem, but cannot be applied in a similar looking problem. I am always sure to draw attention to the two problems so that students can see the slight differences and why they affect the outcome of the problem.

9. In the rote method, students were taught to drop a perpendicular and then apply the memorized solution formula.Transfer Both groups performed well on typical problems asking for the area of parallelograms; however, only the understanding group could transfer to novel problems, such as finding the area of the figures below.or distinguishing between solvable and unsolvable problems such asThe response of the “rote” group to novel problems was, “We haven’t had that yet.”

This is good, and also is the reason I hate teaching my students formulas. I almost always show them and make them practice problems first by figuring out what is going on, rather than giving them a formula. The second I give them a formula, they start blindly plugging numbers in, and cannot complete seemingly simple problems that look slightly different.

10. The concept of adaptive expertise (Hatano and Inagaki, 1986) provides an important model of successful learning. Adaptive experts are able to approach new situations flexibly and to learn throughout their lifetimes. They not only use what they have learned, they are metacognitive and continually question their current levels of expertise and attempt to move beyond them. They don’t simply attempt to do the same things more efficiently; they attempt to do things better. A major challenge for theories of learning is to understand how particular kinds of learning experiences develop adaptive expertise or “virtuosos.”

I like this, I know, and try to make it clear to my students, that I am not a complete expert in my field. It is ok for even me to make mistakes, or to admit that I am unsure about something (as long as I eventually find them the answer). When students see this, I believe they become less self-conscious about making mistakes in front of their classmates. It also helps the more advanced students understand that even they still have a lot to learn.

11. 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 proble

My textbooks often do this, but I try to combat it as much as possible by either assigning problems in review sections that are already mixed up, or at least providing practice where problems are all mixed up before a large assessment. I could never understand why books would organize so many problem sets in ways that allowed students to work through them thoughtlessly.

12. Experts usually mentioned the major principle(s) or law(s) that were applicable to the problem, together with a rationale for why those laws applied to the problem and how one could apply them (Chi et al., 1981). In contrast, competent beginners rarely referred to major principles and laws in physics; instead, they typically described which equations they would use and how those equations would be manipulated

I often notice this in my classroom. I will teach a concept in a way similar to the expert, where I try to focus on the large concept so that students are able to apply that concept in other situations. However, often times when I hear students explaining what I taught to the other students around them, they will only focus on the single method used to solve that exact problem.

13. Research shows that students who think that intelligence is a fixed entity are more likely to be performance oriented than learning oriented—they want to look good rather than risk making mistakes while learning. These students are especially likely to bail out when tasks become difficult

These types of students are always the most challenging for me to teach. I firmly believe that the best way to learn is to try something out, get it wrong, then figure out for yourself why it is wrong and how to fix it. Students that are afraid to be wrong cannot learn in this way until their bad habits are broken.

14. There is no universal best teaching practice.

Could not agree more. I have been most successful when I have blended teaching strategies, or have switched strategies based on the goal of the lesson.

15. This will require active coordination of the curriculum across school years.

I completely agree that this would be the best environment for students to learn, but it has seemed to me very difficult to actually make it happen. Even within school districts there is often little communication between the elementary, middle, and high schools. And even within each level there is not always a natural flow from one classroom to the next. Having teachers keep classes of students for more than a semester or year at a time would help, but that is generally not the case, especially in core subject areas.

16. Experts are also able to fluently access relevant knowledge because their understanding of subject matter allows them to quickly identify what is relevant. Hence, their attention is not overtaxed by complex events.

This is an important skill. So many students seem to think that google can solve all of their problems, therefore they don't have to know/learn as much on their own. But the ability to sift through information and actually determine what is relevant and useful comes from your own understanding of the material.

17. A common misconception regarding “constructivist” theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves.

It seems to me that there always has to be some material where it is very difficult to draw on prior knowledge as it is completely new to students. On these types of lessons, teaching through discovery can lead to more frustration than good. I love to allow my students to discover concepts on their own, but it simply does not work for everything.

18. In the most general sense, the contemporary view of learning is that people construct new knowledge and understandings based on what they already know and believe (e.g., Cobb, 1994; Piaget, 1952, 1973a,b, 1977, 1978; Vygotsky, 1962, 1978). A classic children’s book illustrates this point; see Box 1.2. 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.

Assessing students' prior knowledge is one of the most important tools for a teacher. Being able to relate a difficult concept to a simpler concept that students already understand allows students to come to a much deeper understanding of the content.

19. At the same time, students often have limited opportunities to understand or make sense of topics because many curricula have emphasized memory rather than under- Page 9 Share Cite Suggested Citation: "1 Learning: From Speculation to Science." National Research Council. How People Learn: Brain, Mind, Experience, and School: Expanded Edition. Washington, DC: The National Academies Press, 2000. doi:10.17226/9853. × Save Cancel standing.

I see this as a hard line to walk, especially being a math teacher, it is expected for students to memorize certain properties/equations, where as a teacher your focus has to be on getting the students to understand how and when to actually use the equation, and why it works in the first place.

20. Fundamental understanding about subjects, including how to frame and ask meaningful questions about various subject areas, contributes to individuals’ more basic understanding of principles of learning that can assist them in becoming self-sustaining, lifelong learners.

I agree, I can generally tell more about what a student knows by the questions they ask, compared to anything else. It is also important as teachers to ask meaningful questions to the students, and avoiding simple yes/no type questions.