How People Learn: Study GuideCompiled by EDUC 381 Spring 2007, Brian Beck, & Kym Buchanan

A Cat’s Learning Box –Box 1.1 (pg. 7) Behaviorism-Edward L. Thorndike (1913)–hungry cats learn to pull a string to

open a door to get food. Escape by trial and error Rewards, such as food, increase the connections between stimuli and response. 1950’s cognitive science-approached learning from a multidisciplinary

viewpoint.o Anthropology, philosophy, and computer science

Begin study of mental functioning-about thinking and learning. Recently, realize the importance of social and cultural background of learning.

Learning with Understanding (pg.8-9) New science Students have inadequate chances to study for understanding because many

subjects require students to memorize many different facts. Facts are important, but to apply “usable knowledge” students can connect and

organize significant ideas. –Transfer information. Individuals with a variety of knowledge are more likely to use what they know,

solve problems, and show evidence of transfer.

Pre-Existing Knowledge (pg.10-12) Prior knowledge affects the students’ capability to “remember, reason, solve

problems” and learn new concepts. The current examination of learning is that people develop new knowledge from

what they already know. Some students may be misinformed or given the wrong interpretation in their

lives. Teachers need to concentrate on a student’s partial understandings and limited

beliefs and create ideas to help students become successful.

Fish is Fish (pg.11) Children’s story-by Leo Lionni

o Illustrates dangers of children only building knowledge on prior knowledge without any additional direction.

“Teaching by Telling” works well, but teachers need to give direction when necessary.

Students learn more by sharing prior knowledge –inquiry based instruction

Active Learning (pg.12-13) Students take control of their own learning. Metacognition- “people’s abilities to predict their performances on various tasks

and to monitor their current levels of mastery and understanding.”~This idea focuses on sense making, self-assessment and reflection.

Improves on transfer of information

Complete Understanding

of Learning

Implications for Education (13-19) New science of learning is providing knowledge to increase people’s ability to

become active learnerso Seek understanding of complex subject mattero Relate what is learned to new problems and settings

As educators we should Rethink:o What is taughto How it is taughto How we assess what is learned

An Evolving Science

Scientific Achievements include a deeper understanding of:1. Memory and knowledge structures2. Problem solving and reasoning3. Foundations of learning4. Learning processes (Ex: meta-cognition)5. How the learner’s symbolic thinking comes from the culture and

community he or she lives in.

Even with this deeper understanding we still don’t have the full picture the principles that govern all domains of learning.

Scientific Understanding of Learning

Scientists study Learning

New Research procedures and methodologies

Alterations in current theoretical concepts of learning

Scientific Work

Cognitive & Neuroscience Issues in:

Learning Memory Language Cognitive development

The research is designed to:o Develop explicit computational models

Refine and extend basic principles

Apply models to substantive research questions through: Behavioral experiments Computer simulations Functional brain imaging Mathematical analyses

These studies lead to changes in theory and practice

Key Findings(Note: these findings have strong implications for how we teach and a solid research base to support them)

1. Students come to class with their own ideas about how the world works. If their ideas are not engaged (either reinforced or challenged) they may not learn the material presented in class. Or they will memorize it for a test and then forget it.

“Effective teaching . . . elicits from students their pre-existing understanding of the subject matter . . . and provides opportunities to

build-on or challenge the initial understanding.”

This is true for all ages!

2. To develop competence in an area of inquiry students must:

a. Have a deep foundation of factual knowledgeb. Understand facts and ideas in the context of a conceptual frameworkc. Organize knowledge in a way that allows for “finding” and using it later

Learning with understanding leads to competenceDeep understanding transforms facts into usable knowledge

Organizing information into a conceptual framework allows students to apply what they learned to new situations and to learn related information more easily

3. A “meta-cognitive” approach to instruction can help students learn to take control of their own learning by defining learning goals and monitoring their progress in achieving them.

a. Children can be taught meta-cognitive strategies such as: The ability to predict outcomes Explain things to self to better understand them Note times when they don’t comprehend something Activate/Use background knowledge Plan ahead Apportion time and memory

These things must be incorporated into the subject matter that the students are learning because the processes are not generic; they are

unique to each subject

b. Ultimately the students will be able to prompt themselves and monitor their own comprehension without the teacher support

Self monitoring of understanding: Note when more information is needed Decide if new information is consistent with previous

knowledge Make analogies to increase understanding

Throwing Darts under Water (18-23) 2 groups of children – comparing the effects of learning a procedure with

learning with understanding. 1. Group one received explanation of refraction of light, which causes

deception of the target.2. Group two only practiced throwing the darts. 3. Target was originally placed under 12 inches of water. Both groups did

equally well.

4. When target was moved to only 4 inches below the water, group one did better, from the knowledge given to them.

Implications for Teaching Teachers must draw out and work with the preexisting understandings that

their students bring them. Teachers must teach some subject matter in depth providing many examples

in which the same concept is at work and providing a firm foundation of factual knowledge.

The teaching of metacognitive skills should be integrated into the curriculum in a variety of subject areas.

Bringing Order to Chaos

Designing Classroom Environments (p. 23-26)

Four interrelated attributes of learning environments which need cultivation to better optimize learning…

1. Learner centered schools and classrooms (p.23-24)Teachers must be…-Aware of the knowledge, skills, and attitudes students bring into class

-Sensitive to the variety of differences exhibited by students-Paying close attention to individual progress in order to establish suitable tasks

2. A knowledge-centered classroom environment is focused on what is taught, why it is taught, and what proficiency or mastery looks like (p.24)

-Learning with understanding is essential to the development of expertise -Assess student understanding rather than factual memory (i.e. tests usually reinforce memorization rather than understanding) 3. Assessment-centered classroom environments allow formative assessments to assist both teachers and students monitor progress (p.24-25)

-Students’ thinking is visible to both teachers and students -Assessments should be learner-friendly (i.e. not the Friday quiz) -Allow students to revise and improve thinking -Help students to see their own progress

4. A community-centered approach involves the development of norms for the classroom and connections to the outside world which support core learning values(p. 25-26) -Learning influenced by the context in which it takes place -Norms in the classroom have major impact on student achievement. They must be able to support students’ preconceptions, questions, and progress toward understanding -Cognitive development enhanced by student cooperation and argumentation -Community must support questioning rather than knowing -Students create new ideas that build off one another and gain a sense of ownership -Connect classroom learning to other aspects of students’ lives

Applying the Design Framework to Adult Learning (p. 26-27)

-Principles apply to adult learning as well-Professional development programs for teachers are often: 1. Not learner centered 2. Not knowledge centered 3. Not assessment centered 4. Not community centered

-Principles of learning and their implications for creating effective learning environments apply equally to child and adult learning

-For educational practice to change these principles must also be applied to others, such as policy makers and the public

28-31?

31-36Experts vs. Novices Those who are experienced in certain areas are known to think effectively with

problems in those particular areas. Understanding of expertise is important because it provides an insight into the

nature of thinking and problem solving itself. Experts have acquired extensive knowledge that affects: what they notice, as

well as how they organize, represent and interpret information within their environment which can then affect their ability to remember, reason, and solve problems.

There are key principles of knowledge and its potential implications for learning and instruction:

Experts: notice features and meaningful patterns of information that are not noticed by novices.

~ have acquired a great deal of content knowledge that is organized in ways that reflect a deep understanding of their subject matter. ~ knowledge cannot be reduced to sets of isolated facts or propositions but, instead, reflects contexts of applicability:that is, the knowledge is “conditionalized” on a set of circumstances. ~ are able to flexibly retrieve important aspects of their knowledge with little attentional effort ~ are not always guaranteed the ability to teach others even though they know their disciplines thoroughly. ~ have varying levels of flexibility in their approach to new situations.

Meaningful Patterns of Information One of the earliest studies of expertise showed that the same stimulus is

interpreted differently depending on the knowledge that a person brings to the situation.

Chess Study/ DeGroot (1965) Study

wanted to understand how chess-masters were consistently able to outthink their opponents

Hypothesis: Chess-masters are more likely than nonmasters to: o A) think through all possibilities before making a

move (greater breadth of search)

o B) think through all possible countermoves of the opponent for every move considered (greater depth of search)

- Conclusion: Knowledge acquired over tens of thousands of hours of chess playing enabled the masters to out-play their opponents: Recognize meaningful chess configurations while also realizing strategic implications of these situations

- Observations: Chunking/ Experts have the ability to chunk information into meaningful patterns which is then perceived.

Affecting the memory of what they see.

Other Examples Expert skills have been demonstrated in other domains as well including:

1. Electronic Circuitry 2. Radiology 3. Computer programming 4. Mathematics 5. Teaching

Final Thoughts: Acquiring greater competence requires an increased ability to segment the

perceptual field. It is important to provide students with learning experiences that specifically

enhance their ability to recognize meaningful patterns of information.

ORGANIZATION OF KNOWLEDGE Pgs. 36-42

Expert Organization1. Is NOT centered on a list of facts and formulas2. IS centered on Core Concepts and Big Ideas

Novice Organization

1. Is the exact opposite

Physics Experiment1. Experts set out a plan focusing on major principles (Newton’s 2nd Law)2. Novices simply tried to plug numbers in equations

Pause Times1. Novices appear to retrieve information in a sequential memory search2. Experts seek out sets of related equations with meaningful relations

FINAL OBSERVATIONS…1. Novices tend to be more superficial while experts formulate reasonable

interpretations and look past the problem2. This is very similar to “thinking outside the box”

3. Looking at most current academic curricula the problem seems to be that we are teaching “a mile wide and an inch deep”

1. Based on this knowledge this is a poor way of going about developing the competencies that prepare students for future education and work

BOX 2.2 Pg. 37

Expert and novice teachers notice very different things1. Novices have the ability to see what is going on in a class2. Experts have the ability to know why the students are acting in a certain way

1. Examples1. Novice: Students are getting ready for class2. Expert: The students are used to this format and setting

FINAL OBSERVATION…1. Novices try to read the minds of students while experts look at physical signs

such as facial expressions

Understanding and Problem Solving (41-45)-In Mathematics experts more likely than novices first try and understand a problem before attempting it.-In a study, Experts and Students were asked to solve a word problem

-Experts realized problem was logically impossible-Some students realized this as well but others tried to solve the problem

-Most children try to provide some kind of numerical answer to problems.

Context and Access to Knowledge-Experts have a lot of knowledge in their field but only a small portion of it is relevant.

-Experts are good at retrieving relevant knowledge for a specific task.-This knowledge is called “conditionalized.”-Knowledge that is not conditionalized is called “inert” because it is not

activated.-Concept of conditionalized knowledge is useful in:

-Design of a curriculum-Instruction-Assessment practices that promote effective learning

-Many forms of curricula and instruction don’t help students conditionalize knowledge.

-It is left to students to generate condition-action pairs to solve problems.

-To help students learn about conditions should require them to use appropriate concepts and formulas.

-If done right students will learn appropriate ways to use knowledge (can fail).

-The concept of conditionalized knowledge has important implications for assessment practices that provide feedback about learning.-Many types of tests fail to help teachers and students assess how much of their knowledge is conditionlized.

Fluent Retrieval-People’s ability to retrieve relevant knowledge can vary from effortful to relevantly effortless to automatic.

-Automatic and fluent are important characteristics of experts.-Fluent retrieval doesn’t necessarily mean you will do a task faster; you could spend more time thinking about the task than actually doing it.-Fluency is important because effortless processing places fewer demands on conscious attention.

-Issues of fluency are important for understanding learning and instruction-Important for students to become fluent at recognizing problem types so appropriate solutions can be easily retrieved from memory.

Experts and Teaching-Just because you’re an expert doesn’t mean you’re a good teacher.

-Being an expert can hurt your teaching because you may not realize what is easy and difficult for students.-Content knowledge in teaching needs to be different from pedagogical content knowledge to provide effective teaching.

-There are difficulties students have while learning a topic, typical paths students follow while learning, and set strategies to help students learn.-Shulman argues teaching strategies differ across disciplines.-Expert teachers know difficulties students face, how to tap into their knowledge to make it more meaningful, and how to assess student’s knowledge.-Expert teachers have acquired pedagogical content knowledge as well as content knowledge.-Textbooks are used in the absence of pedagogical knowledge but textbooks don’t know the students difficulties.-Pedagogical content knowledge is a very important part of what teacher needs to learn to be more effective.

Adaptive Expertise (p.45-48)

Some ways of Organizing Knowledge may be better at helping people remain flexible and adaptive to new situations than others.

The challenge at hand is to figure out how particular types of learning experiences develop adaptive expertise.

To be flexible in new situations one must use metacognition, which allows him/her to think about his/her own understanding/thinking, and decide when it is inadequate.

Some Big Ideas:

• Some children wrongfully believe that they can remember information, and as a result they do not use strategies such as studying that will help them remember/retain the information.

• Beliefs about what it means to be an expert can affect the degree to which people search for what they do not know and take steps to improve a situation.

• Some people believe that an expert is someone who knows all the answers. When looking at it from this perspective, it can limit new learning.

• Switch from “answer filled experts” to “accomplished novices,” meaning that “accomplished novices” are skilled in many areas, but they realize that what they know is a small amount compared to all there is to know.

Teaching Hamlet Box 2.4 (p.46-46)

There are different ways to teach the same topic.

Not everybody learns in the same way.

Some Big Ideas:

• Teachers need to look at situations from their students’ perspective.

• It may be helpful to have students make connections with themes and issues similar to a new topic prior to introducing the new topic.

Conclusion (p.48-50)

Pattern recognition is an important strategy that helps students develop confidence.

Understanding when and where to use information is important. The ability to retrieve information effortlessly places fewer demands on conscious attention which has a limited capacity. Effortful retrieval places demands on conscious attention so effort is placed on remembering rather than learning.

Adaptive expertise raises the question of whether certain ways of organizing knowledge leads to increased flexibility in problem solving.

Metacognition is an important aspect of competence. Having the ability to think about ones’ own understanding and decide if it is inadequate is an important skill.

Some Big Ideas:

• Curricula that emphasizes breadth of knowledge may prevent the effective organization of knowledge because there is not enough time to learn anything thoroughly or in depth.

• Expertise in an area does not guarantee that one can effectively teach others about that subject area.

(51-55)A.Learning and Transfer 1.Learning and transfer of learning help understand how people develop important competencies

-transfer of learning-ability to use what was learned in one context to new contexts

-main goals of transfer-one problem to the next-school year to school year-school to home/workplace

Big Ideas: “It is better to broadly ‘educate’ people than simply ‘train’ them to perform particular tasks.”

2.Measure of transfer shows quality of people’s learning experience-when focusing on remembering-learning experiences look the same-types of learning experiences

-good memory but poor transfer-good memory and good transfer

3. Thorndike-first to use transfer to test assumptions about learning-Doctrine of “formal discipline”

-learning Latin and other difficult subjects lead to development of general skills of learning and attention-discovered learning is not like developing a “mental muscle”-learn more specific things

-transfer between initial and later learning-based on match between the elements of the two

-specific facts and skills-example: skills in writing letters of alphabet lead to skills in writing words

-transfer from school subjects to non-school settings-teach knowledge and skills that have elements identical to activities outside of school

-negative transfer-experience from one event can hurt performance on related tasks-modern theories of learning and transfer-emphasis on practice that uses existing knowledge and strategies

4.Key characteristics of learning and transfer:

-initial learning is needed for transfer with large amounts of experience to support transfer-overly contextualized knowledge reduces transfer-abstract representation promotes-active, dynamic process vs. passive end-product of a set of learning experiences-new learning involves transfer based on previous learning

-creates design of instruction to help students learn

B.Box 3.1 What People Learn 1.Experiment-increasing a college student’s digit string retention capacity

-started with 7 digits-worked up to 70+

-chunked into meaningful groups-used vast knowledge of winning times for famous races to chunk large strings

-letter strings-returned to seven digits

C.Elements that Promote Initial Learning 1.initial learning

-used studies designed to assess effects of learning to program in computer language LOGO

-hypothesis: students who learn LOGO transfer this knowledge to areas that use thinking and problem solving-tests showed no such transfer

-later tests paid attention to degree of LOGO learned-transferred to related tasks once students learned an adequate level of LOGO

Box 3.2 – An Example of Negative Transfer (pages 54-55)Luchins and Luchins performed a test to demonstrate how previous experience can sometimes make it more difficult when transferring to a new situation

Experiment included giving participants three jars of varying sizes and asking them to obtain a specified water amount

Everyone received a practice problem Experimental group were given 5 additional practice problems before

proceeding to the test problems Control group were given test problems immediately after the original practice

problem The practice problems in the experimental group were designed to teach this

group a specific way of obtaining the desired results After the practice problems, participants in the experimental group were more

likely to use the method they were taught to solve the test problems even though there were easier methods of solving the problem. Those in the control group were able to perform the test problems quicker because they did not have any preconceived notions that inhibited their ability to solve the problem in the fastest way possible. Therefore, participants in the

experimental group “negatively transferred” their method to the test problem, causing slower times than the control group.

Understanding Versus Memorizing (pages 55-56)The ability to transfer knowledge is also affected by the extent to which people learn with actual understanding as opposed to just memorization of facts

Simply remembering something is not the same as understanding its concept and intricacies

The ability to transfer knowledge is increased with comprehension of the idea

Box 3.3 - Throwing Darts (page 56)Two groups of children practiced throwing darts at a target underwater

One group was taught about refraction of light and how it affects what you are seeing through water (the target looks deceptive) and practiced dart throwing

The other group only practiced dart throwing and was given no lesson on refraction of light

Both groups performed equally well on a practice task involving a target under 12 inches of water

The group given information about refraction did much better in a task where the target was only under 4 inches of water because they could transfer the knowledge they learned about refraction to aid them in throwing the darts

Time to Learn (pages 56-58)It takes time to learn complex subject matter

It requires a great deal of time to become an expert at something. Even those who are “talented” need extensive amounts of time to become masterful in the area.

The amount of time it takes to learn something is proportional to the amount of material being learned

It is difficult for students to learn some things because they do not yet understand the underlying concepts

Teacher should be wary about covering too many topics too quickly because students need time to integrate each area into their current patterns of understanding.

Students also need time to process information – short-term memory is very limited.

Pg. 57 Figure 3.4 Finding the Area of a Figure

Three different methods are used to convey the idea.1. Understanding method2. Rote method3. Transfer

Some combinations of these methods are better than others. Transfer of knowledge was more evident in the “Understanding” group than in the

“Rote” method group.

The students who actually understood the “why” and “how” were better equipped to solve the problem of an area of a figure when it was not a typical shape than those who had memorized a formula and only knew a set of rules to solve a practiced problem. - Who actually learned?

Big Ideas: Students must understand “why” and “how” and be able to transfer knowledge to new situations to have truly learned.

Pg. 58-60 Beyond “Time and Task”

Learning is most effective when people engage in “deliberate practice” Feedback is traditionally identified as important for successful learning but is not

a unidementional concept.1. Feedback signaling progress for memorization of facts.2. Feedback signaling the state of the student’s understanding.

Understanding when, where and why.1. Students need this to know how to use the knowledge they are learning2. Can be enhanced through ”contrasting cases”

Contrasting cases highlight points that may have been missed before. Appropriately arranged contrasting cases apply to perceptual and conceptual. Transfer of knowledge is enhanced by helping students see potential transfer

implications of what they are learning. 1. LOGO programming2. Students weren’t taught to memorize procedures of programming, but to

generate a clear, bug free program

Big Ideas: Use different methods of feed back to gauge the students’ understanding.

Pg. 58 Box 3.5 “Learning Algebra”

Students who were taking regular algebra received an average of 65 hours of instruction.

Students in the advanced algebra classes receive 250 hours of instruction. What are the expectations of each of the classes and did the school invest

enough time into the regular algebra class?

Big Idea: Significant learning takes significant investment.

Pg. 60-62 Motivation to Learn.

According to White (1959) students have “competence motivation”1. Students are motivated to develop competence.2. Students have extrinsic and intrinsic motivations.

1. Intrinsic motivation is the desire to do the activity for its own sake. 2. Extrinsic motivation is desiring to do something for the sake of

some external catalyst.

Keep motivation at a proper level of difficulty.1. i.e. Design the Experience!

1. Too easy is boring2. Too difficult is frustrating3. Both situations are ineffective in designing a good learning

experience. Keep in mind who your students are.

1. Performance oriented will worry more about making the grade than learning. So if it is too difficult will shut down and not learn.

2. Learning oriented like new challenges.3. The orientation will change across different disciplines.

Social opportunities also affect motivation.1. Feeling that one is contributing something to others appears to be

especially motivating (Schwartz et al., 1999) Students are more motivated when they see the usefulness of what they are

learning.1. Ex. “When am I ever going to use Algebra????”2. When asked what the highlights where from the year before, 6 th grade

students from an inner city school frequently mentioned projects that had social consequences.

1. Designing playhouses.2. Presenting the blueprints for the playhouses.

The students had to learn geometry and architecture to build the playhouses, then present them to professionals who would hold them to high expectations.

Big Ideas:

Design the experience. Stay in the “Wobbly Place” but don’t be the training wheels!

Students are motivated in different ways, so know your students motivations and link the material to be learned with real life.

1) Box 3.6A) 3 groups of students received different types of instruction on schema theory and memory.

1. Group 1: Read and summarized text and then listened to lecture to help organize thoughts and gain a better understanding.2. Group 2: Did not read text but actively compared data. Then listened to same lecture as group 1.3. Group 3: Spent twice3 as much time as group 2 working with data, but did not listen to the organizing lecture.

B) Results1. Group 2 performed much better than groups 1 and 3.

a. Actively working with data helped them learn from the lecture.2. Lecture was necessary.

a. Proven by poor performance of group 3.

2) Other Factors That Influence Transfer (Context) pages 62-63A) Transfer across contexts is difficult when a subject is taught in a single context rather than a multiple contexts.

1. One frequently used technique is to get learners to elaborate on example used during learning.

a. Could potentially make it more difficult to retrieve taught information in other contexts because knowledge tends to be more context –bound when learners elaborate new material with details of the context in which material is learned.

2. When concepts are taught in multiple contexts, learners are more likely to grasp the concepts and develop a flexible representation of knowledge.3. Findings from instructional programs using case based and problem based learning indicate that if students learn only in this context, they often fail to transfer flexibility to new situations.4. Way to deal with lack of flexibility.

a. Ask learners to solve a specific case and then provide them with an additional similar caseb. Let students learn in a specific context and then help with “What if” problem solving designed to increase the flexibility of their understanding.c. Generalize the case so learners are asked to create a solution that applies not to a single problem, but a whole class of related problems.

3) Problem Representations (page 63)A) Transfer is enhanced by instruction that helps students represent problems at higher levels of abstraction

1. Can help increase probability of positive transfer and decrease the degree to which a previous solution strategy is used inappropriately.2. Research has shown that receiving abstract learning enables learners to think flexibly about complex domains.

4) Relationships between learning and transfer conditions (pages 63-66)A) Whether student will transfer across domains (subject areas) depends on whether they receive successful transfer or unsuccessful transfer.

1. Singley & Anderson (1989) ague: Transfer between tasks is a function of the degree to which the tasks share cognitive elements.2. Biederman and Shiftrar (1987): Provided strong support for the benefits of helping students represent their experiences at levels of abstraction that transcend the specifics of particular contexts and examples.

B) Memory retrieval and transfer are promoted by schemata because they derive from a broader scope of related instances than single learning experiences.

Pgs 64-69

Box 3.7 Flexible Transfer2 General and Fortress3 Doctor and malignant tumor4 90% of students couldn’t solve doctor problem until being told to compare it to

general story5 BIG IDEA: When connection between two sets of information is explicitly pointed

out, problems are easier solved.

Active vs. Passive Approaches to Transfer6 Transfer- a dynamic process that requires learners to actively choose and

evaluate strategies, consider resources, and receive feedback7 Not based on initial performance, transfer based on second day of learning8 Transfer better with prompting9 “graduated prompting”-amount of help needed for transfer by counting number of

prompts needed before a transfer is made

Transfer and Metacognition10 Reciprocal teaching- instruction and practice, provision, social setting that

enables joint negotiation for understandingo Students and teacher take turns leaning group to discuss strategies for

understanding and remembering11 Procedural facilitation- prompts learners to adopt to metacognitive activities

embedded in subject strategies12 Alan Schoenfield- taught mathematical problem solving to college students

o Modeling, coaching scaffoldingo As teacher fades out, students ask self-regulatory questions to themselves

13 Emphasis on metacognition engages students as active participants in learning and evaluating own progress toward understanding

Learning as a Transfer from Previous Experiences14 “all learning involves transfer from previous experiences”15 Students may have previous relevant knowledge that is not yet activated16 Students may misinterpret new information because of previous knowledge17 Students may have difficulty with particular school teaching practices that

conflict with community practices

Box 3.8 Everyday and Formal Math 18 Fasheh’s mother used math in a way that was basic to her operation of

understanding: order, pattern, relations, measurement

19 Mistakes in her math entailed practical consequences, unlike mistakes in Fasheh’s math

Building on Existing Knowledge p.69It is important to consider what existing knowledge the student carries with them from everyday life that can be used to learn abstract ideas such as arithmetic.

By tapping into the existing knowledge of the student, the teacher can aid the student in “acquir[ing] a more coherent and thorough understanding of [the lessons] than if they taught them as isolated abstractions.”

Understanding Conceptual ChangeWhile learning involves transferring prior knowledge, this prior knowledge can make it difficult to learn new information. Confusion aids the student in identifying the incongruence between their existing knowledge and the new information. A problem arises when students use prior knowledge to formulate their own understanding of the new information in an erroneous way and don’t recognize the misunderstanding. Examples: Chapter 1 Fish is Fish and the Spherical Flat Earth

Kym Bulletin: “Children’s interpretations of the new information are much different that what adults intend.”

Failing to probe a student for prior misconceptions when teaching a new idea or building on an existing idea can amplify the problem and perpetuate further misunderstandings while keeping the student from a clear understanding of the concept. Examples: Physics – forces on objects; Biology – food for plants and photosynthesis

Assumptions children make when learning the fundamentals can hurt their understanding of more complex concepts. Example: Math is counting can hurt understanding of rational numbers.

“Teaching by telling” can perpetuate some of the above problems with using existing knowledge. While lectures under the right circumstances can be useful, making a student’s thinking visible helps them to identify and re-think misconceptions.

Transfer and Cultural PracticesKnowledge learned as a result of the culture in which a student lives can both hinder and accelerate a student’s learning in school. This type of prior knowledge is not attributed to developmental stages or personal experiences (i.e travel or parents’ jobs).

Kym Bulletin: “School failure may be partly explained by the mismatch between what students have learned in their home cultures and what is required of them in school.”

Teachers often (mis)judge the intelligence and academic capabilities of a student by their readiness or resistance to answer what may seem like obvious questions (depending on their home experiences).

Cultural differences between mother and infant interactions such as either asking about an object or asking to evaluate an object plays a role in the broad set of skills that a student may bring with them to the classroom, and how the students react to changes in context.

The transfer of learning between mother and child is also culturally bound. African American students usually write in topic-associative oral stiles compared to white children who tend to write in a linear expository style. Ironically (or not so) the linear expository style is most often taught in schools and view students who use the topic associative oral style as lower academic achievers.

Kym Bulletin: “Teachers can be helped to view different cultural backgrounds as strengths to be built on, rather than as signs of ‘deficits.’”

Box 3.9 Eating Pie and Learning Fractions p.72

This box cautions against using “commonplace” examples in learning activities. For students who are unfamiliar with the “commonplace” item, they become more interested in what the item is rather than what the activity is about. In this case, the teacher is trying to help the students learn fractions by using pumpkin pie as a model for how fractions are part of a whole. One of the students is unfamiliar with what pumpkin pie is (being of African American decent, sweet potato pie is the commonplace) and becomes focused on what pumpkin pie is, rather than the lesson at hand: Fractions.

Transfer between School and Everyday Life

(P 73-77)

2 The ultimate goal of learning is to have access to information from a wide set of purposes

3 The learning will in some way transfer to other circumstances

4 The ultimate goal of schooling is to help students transfer what they have learned in school to everyday settings of home, community, and workplace.

5 An important strategy for enhancing transfer from schools to other settings may be to better understand the nonschool environments in which students must function

6 Important to explore ways to help students develop the characteristics of adaptive expertise

7 Three Major Contrasts between everyday settings and school environments

o One is that the latter place much more emphasis on individual work than most other environments

navigation on U.S. ships found no individual can pilot a ship alone, it takes a collaboration of people working together

o A second one is the heavy use of tools to solve problems in everyday settings, compared with “mental work” in school settings

Helps people work almost error freeNew technology makes it possible for students to use tools that most likely is used by professionals in workplaces

o A third one is that abstract reasoning is often emphasized in school, whereas contextualized reasoning is often used in everyday settings

Reasoning can be improved when abstract logical arguments are embodied in concrete contexts

8 The most effective transfer may come from a balance of specific examples and general principles

Summary and Conclusion(P.77-78)

9 a major goal of schooling is to prepare students for flexible adaptation to new problems and settings

10 the ability of students to transfer provides an important index of learning that can help teachers evaluate and improve their instruction

11 students are motivated to spend the time needed to learn complex subjects and to solve problems that they find interesting

12 In order for learners to gain insight into their learning and their understanding, frequent feedback is critical: students need to monitor their learning and actively evaluate their strategies and their current levels of understanding

13 With multiple contexts, students are more likely to abstract the relevant features of concepts and develop a more flexible representation of knowledge.

14 In assessing learning, the key is increased speed of learning the concepts underlying the new material, rather than early performance attempts in a new subject domain

15 All new learning involves transfers16 Help learners choose, adapt, and invent tools for solving problems is one way to

facilitate transfer while also encouraging flexibility

The Cottage Cheese Problem(Box 3.10 P.75)

17 A man who needed three-fourths of two-thirds of a cup of cottage cheese to create a dish he was cooking. He did not attempt to multiply the fractions as

students would do in a school context. Instead, he measured two-thirds of a cup of cottage cheese, removed that amount from the measuring cup and then patted the cheese into a round shape, divided it into quarters, and used three of the quarters

Three Solutions to the Best-Buy Problem(Box 3.11 P.76)

18 Grocery store shoppers use nonschool mathematics under standard supermarket and simulated conditions

(79-84)

Infants Capabilities

Originally thought that a newborn baby’s mind was a blank slate.1. Experience is gradually impressed on the mind2. Was assumed that language was a necessity in abstract thought

New Ideas1. 1920’s Piaget – idea that the young human mind is cognitively complex

and develops in stages2. Babies develop physical awareness by seeking environmental stimulation

Zone of Proximal Development Vygotsky (1978)

3. Distance between the actual developmental level and the level of potential development.

4. Under guidance of adults or more capable peers5. Big Idea: What a child can perform today with assistance, they can

perform tomorrow on their own.

Methodological Advances

New methods to measure what babies know:

6. Non-nutritive sucking – pacifier is hooked up to a screen that brings the picture in and out of focus – babies quickly learn to suck the pacifier at a certain rate to keep the image in focusBig Idea: Infants can quickly learn to control their own environment.

7. Habituation – babies that are presented with an event (picture, sound, movie) will lose interest if there is no change after a extended amount of time, but, their interest returns if the event changes slightly

Big Idea: Infants can distinguish small discrepancies in an event. They also have a certain attention span.

8. Visual Expectation – A flashing pattern is developed by flashing one side of a screen for a count, then the other for another count. For instance, the left side of the screen flashes twice, then the right flashes three times. The infant’s eye gaze begins to anticipate the flashes.

Big Idea: Infants are able to understand basic patterns and rhythms. By following the pattern, the infant exhibits the ability to count.

Early Competencies in the Privileged Domains: Physical Concepts

(p. 84-88)1 Infants as young as 3 months have the beginnings of useful knowledge such as

understanding that objects need support to prevent them from falling2 Study shows that infants observe impossible events longer than possible events3 Infants also observe physically inconsistent events longer than the ones that are

consistent with the infants expectations4 Infants as young as 2-1/2 months understand that when stationary objects are hit

by moving objects they themselves move and by 6-1/2 months then understand the size of the moving object has a larger impact on the stationary object distance moved

5 At 9 months a child can discover that they can bring toys near themselves with objects such as a blanket, box, or table cloth

6 Although it is not until a child is 24 months old that they can pick the right tool to reach an object

Big Ideas7 Point of contact8 Demonstrations are needed for better understanding

Biological Causality (p. 88-89)9 Infants learn at a very young age the difference between inanimate and animate10 Inanimate objects need to be propelled or pushed into movement11 Young children show an understanding that if they are made of “biological stuff”

they can move themselves12 Young children can give an answer to the differences between insides and

outsides of animals verses machines and inanimate objects Big Ideas:

13 At a young age children can construct rational accounts

Early Number Concepts (89-91)

2. Human mind has the ability to facilitate attention to the number of items in a visual array.

a. Examples (drumbeats and jumps of a toy bunny (2-4 jumps)3. 6-8 month olds showed 2 or 3 item displays; ½ shown 2, ½ shown 3

b. Looking times dropped by 50% once they became bored.c. When display showed different number of items than before the interest

was regained.d. Big Idea: They are able to process information that represents numbers at

a rather abstract level.4. Young infants and toddlers respond correctly to the effects of arithemetic

operations (adding and subtracting)e. Children can tell when an item is added or subtracted from what they

expect.f. Train them to see two objects, they show them they are adding one so the

child expects 3 and not 1.g. Big Idea: Children are actively engaged in using their implicit knowledge

of number to attend to and make sense of novel examples of numerical data in their environments.

Early Attention to Language (91-95)

5. Children have the ability to understand their own world using physical and biological concepts.

a. Infants also have this same trait to learn language.b. At 4 months infants prefer listening to words rather than other sounds.c. They are able to distinguish between languages.d. Infants pay attention to features of speech (intonation and rhythm).e. Learning environment is critical.f. Attracted to faces, especially the lips of a speaker.

6. Apple Experiment done on a 13 month old child.g. Told to eat the apple while in a highchair

i. Child bit the apple.h. Told to throw the apple while in a playpen.

i. Child threw the apple.i. Told to eat the apple while in the playpen.

i. Child threw the apple.j. Told to throw the apple while in the highchair.

i. Child bit the apple.k. Big Idea: Child assumed what they usually should do in the situation

i. Highchair-eatii. Playpen-play or throw

l. Big Idea: The child uses meaning as a clue to language rather than language as a clue to meaning. Experience and use of the skills are important. This needs to be an active process

Page 92) Box 4.2

An experiment shows how three- to five-year-old children do mathematical reasoning: The experimenter starts out with five toy mice on a plate. Without the child noticing, the experimenter removes a number of mice. The child reacts by trying to remember where the other mice had been. He decides that to “fix the game…some [of the mice] might have to

come back.” The child puts four mice back, decides that there are too many, and

takes some away, ending up with five mice as he had at the beginning.Page 95)

Strategies for Learning and Metacognition:

Big Idea: “In order to thrive, children must…engage in self-directed and other-directed learning, even in areas of early competence.”

Scientific research in recent years has shown that children possess strategic competence and metacognitive knowledge.

I. Views of Learning:

Traditional view of learning: Young children have little knowledge and are incapable of much, but as they grow older and gain experience they develop competence: “Learning is development and development is learning.”

Alternative view of learning: This view of learning takes into account first that information processing is used to explain developments in children’s learning. This view also takes into account that all humans have limits in their short-term memory storage.

Page 96)

Big Idea: According to the view based on these principles, then, development means overcoming information-processing constraints.

Psychologists ask: Do children have less information processing skills than do adults?

-One view of learning in children is that they have less memory capacity than adults do.-Alternatively, there is a view that children have the same memory capacity as adults do, but that they develop skills and strategies to remember better as they get older.

Strategies for Memory Storage:

Clustering

1. This strategy helps humans to remember seemingly unimportant pieces of information in meaningful groups, especially groups of five, seven, and nine.

Chunking1. Remembering groups of more nine items proves to be difficult. To

overcome this limitation, people group items together into sets of letters, pictures, or numbers that have meaning for them.

Page 97)

Metacognition involves: 1. Knowledge of one’s own learning strengths and weaknesses.2. The ability to reflect on one’s own performance so that one can self-

regulate and plan.3. Self-regulation and reflections.4. Gradual development over time.

Page 98)

The study on page 98 describes a group of three- and four-year old children’s strategies to help them remember information.

An experimenter shows the children, one at a time, a toy dog. He then hides it under one of three cups. He tells the child to remember which cup the dog is under and leaves the room for some amount of time. While the experimenter was gone, the children each used strategies to remember where the dog was.

These include mnemonic strategies and retrieval cueing. One mnemonic strategy was to look at the target cup and nod yes. One retrieval cue strategy was to move the correct cup away from the others.

Big Idea: Without some effort in self-regulation and planning, people will forget information.

Reading Guide 98-102Multiple Strategies, Strategy Choices

- Strategies used by children to memorize, conceptualize, reason and solve problems grow increasingly effective and flexible

strategies are not solely related to age children of same age use wide variety of strategies children will use different strategies on different daysEx) 3 + 5

Preschool – add up from 16-8 yr old – add by counting from larger number9 and Up – retrieve answer from memory

- the broader the range of strategies the more precisely children can shape their approaches to situations

- Young children can use the strengths of different strategies, and use the one with the best advantage for different situations

Ex) 4+1 likely to retrieve answer 2+9 count from larger # 6+7 count from 1

-Microgenetic Studies- can identify when a new strategy is first used- 3 key findings

1. Discoveries are often made in the context of successful performances

2. Short-lived transition strategies often precede more enduring approaches

3. Generalization of new approaches often occurs very slowly- Understanding of children’s strategic development has led to instructional initiatives

- Reciprocal teaching- Community of learners- The ideal student- Project Rightstart

Box 4.3 Remembering where Big Bird is-18-24 month children- Big Bird was hid in various places in the room- Children were told to find Big Bird when the bell rings- Children were focusing on Big Bird while they were playing and waiting

“Big Bird hiding”“Me find Big Bird”

- Used a less systematic rehearsal strategy to keep the information alive

Multiple Intelligences- Gardner proposed 8 forms of intelligence- Linguistic, logical, musical, spatial, bodily kinesthetic, interpersonal, intrapersonal, and naturalistic (newest form of intelligence)- Linguistic and logical are typically used on tests and valued in schools- Some educators believe that all children should have each intelligence nurtured- Some educators focus on development on specific intelligences- Multiple intelligences offer many different approaches to the subjects being taught.

Motivation to Learn and Understand- Children have their own conceptions about their minds, and how people learn and are intelligent- There are two beliefs: entity theories and incremental theories-Entity Theory

- children believe that intelligence is a fixed property in individuals- hold performance goals in learning situations- strive to perform well, attain positive judgments- avoid challenges that will make them look bad- little persistence in the face of failure

- Incremental Theory- children believe that intelligence is malleable- intelligence can be improved with effort and will- regard their own increasing competence as their goal- seek challenges and show high persistence

- Children’s theories about learning affect how they learn and how they think about learning

Big Ideas-Teachers can guide children to a more health conceptualization of their learning potential if they understand the beliefs that their students have.-Good reasons exist for people to know and use multiple strategies.

Pgs. 102-104, Box 4.4 I. Self-directed and Other Directed Learning

A. Achievement or Competence Motivation (in children)1. Strong desire to apply themselves in intentional learning situations2. Learn in situations with no external pressure to improve or reward other

than satisfactionB. Problem solvers and Problem Generators

1. Seek and create challenges2. Adult w/ crossword vs. child w/ jigsaw

BIG IDEAS: A challenge in schools is to build on children’s motivation and harness it in the service of learning.

II. Guided Children’s LearningA. Infants and Toddlers

1. First 4-5 yrs complimented by adult-child relationships2. Model mature performance during activities3. Arrangement of the child’s environment

BIG IDEAS: Caregiver to child communication to accomplish everyday goals is the groundwork for children’s early learning of the language and other cognitive tools of their community.

B. Connections1. Connect new situations to more familiar ones2. Relevant knowledge is not always accessed

C. Scaffolding1. Interesting the child2. Reducing the number of steps3. Maintaining the pursuit of the goal4. Marking critical features5. Controlling frustration6. Demonstrating and idealized version

BIG IDEAS: Effective teachers help people of all ages make connections among different aspects of their knowledge.

Box 4.4 Solving a Problem

Cups were previously nested together but given to children un-nested. “These are for you to play with”. Children try to nest them together without being told to do so. Young children try to use force to complete the task without changing how they go about solving the problem. They develop to making limited changes and finally to looking at the problem as a whole.

BIG IDEAS: Children are persistent because success and understanding are motivating on their own.

Which Toy? (Box 4.5 page 105) Adult and infant looking for toys. Many trial and errors. Finally find the right toy.Learning to Read and Tell Stories (Pages 105-108) How is it that children born with no language learn to tell stories within the first

three years? Early reading/story telling with parents is very important for language

development.Alice in Wonderland Reprinted in the late nineteenth century as a nursery rhyme. Subtext aimed at adults but the pictures tell the story. Adults are supposed to tell the story: Alice in a pool of tears example. Adults must guide young children’s attention and invoke curiosity. Engage the child in dialogue even if it is limited at first.Reading with young children Mother started “reading” at 8 months old and changed her expectations as her

son learned more: “What’s that?” Mother updated constantly to keep up with his new vocabulary. Adults can ask more questions and add more information as children get older:

“That’s right that’s a beehive. Do you know what bees make……” Use the material to provide more background knowledge: comprehension

fostering activities will be helpful later in life. These reading activities function in the child’s zone of proximal development. With the “wobbly place” adults must continue to increase collaboration with the

child as the child’s understanding gets greater.Children as Narrators By age three or four children are telling stories. Children like to learn scripts: going to bed or going to McDonalds. Everyday experiences foster story telling. As children get older they increase the elements to their stories and in joint story

telling, they can even be the leaders.

Connection making and building scaffolds helps the children later in life with skills such as math.

Baby Reading (Box 4.6 page 106) Grandfather “reading” a picture book of mothers and babies to distract child from

mother’s absence. “Kanga, baby” reference to Winnie the Pooh and giant kangaroo stuffed animal:

“Where’s Julie’s Kanga?” Even at one word utterance stage children can “read,” “refer,” and

“represent.”