Skip to main content

Home/ ETAP640/ Group items tagged math-problems

Rss Feed Group items tagged

11More

JTE v24n1 - Transfer of Learning: Connecting Concepts During Problem Solving - 0 views

  • There are several factors that affect learning transfer. These include whether students understand or simply memorize knowledge, the amount of time spent on learning the task, the amount of deliberate practice that is done beyond learning the task, the motivation of the student, how the problem is represented, the transfer conditions, and the metacognition of the solver (Dweck, 1989; Ericsson, Krampe, & Tesch-Romer, 1993; Johnson et al., 2011; Palinscar & Brown, 1984; Singley & Anderson, 1989).
  • A student’s comprehension of a problem and his or her ultimate ability to transfer concepts learned previously to the current problem is inextricably linked to his or her ability to properly represent the problem.
  • ognitive research shows that the organization of learning and how new learning relates to what a student already knows are the strongest predictors of how well a student will transfer knowledge (National Research Council, 2000). Schunn and Silk (2011) articulated, however, that in science and engineering students often “lack relevant conceptual frameworks or have frameworks that are not developed enough to support new learning adequately” (p. 9). The absence of such frameworks makes it difficult for students to connect and apply other knowledge where relevant.
  • ...8 more annotations...
  • The problem solving process begins as soon as the problem solver generates enough information about the problem space to gain an understanding of the problem.
  • Representation in the problem-solving process refers to how the solver mentally represents the problem. The solver’s representation of the problem is directly related to his or her existing knowledge structure of the content of the problem.
  • Students have to increase their reflective practice to aid their metacognition and transfer of STEM concepts.
  • Different individuals have different conceptual knowledge and will make different associations to their knowledge. Exposure to the constraints and affordances of a particular context in which a problem exists will invariably influence the way in which the student represents a problem in a similar context.
  • Sanders (2009) admitted that it is difficult to prepare a teacher that is competent in all three bodies of knowledge, given the volume of content knowledge necessary to be an effective science, mathematics or technology educator.
  • This pedagogical approach is not without its challenges, as students may still compartmentalize their knowledge. Also, it is often difficult logistically and in terms of instructional timing for teachers across STEM discipline to collaborate effectively (Crismond, 2011; Kimbell & Stables, 2008).
  • Good and poor problem solvers differ in their recall of information from previously encountered problems and by extension their ability to transfer concepts to the target problem. This difference exists because poor problem solvers tend to remember surface similarities between problems, while good problem solvers remember underlying conceptual structures that make two problems similar although they have different surface features (Sutton, 2003).
  • Until student assessment methods are modified to reflect less dependency on standardized tests, engineering and technology educators will garner greater collaboration from math and science teachers when the latter can see that engineering and design-based curriculums does improve students’ ability to solve standardized test problems.
1More

Mr. Robb's Math - Hundreds of Math Videos - 1 views

  •  
    Mr. Robb's Math is a YouTube channel containing 555 videos produced by high school mathematics teacher Bradley Robb. Mr. Robb's videos explain and demonstrate solving problems in Algebra I, Algebra II, and Calculus. Most of the videos are recorded while Mr. Robb is teaching. You can find the videos on the Mr. Robb's Math YouTube channel or visit Mr. Robb's website WowMath to find the videos organized in sequence with accompanying screenshots.
3More

Unshielded Colliders: Poverty and Education - 0 views

  • For example, Mel Riddile points out that when one conditions on various measures of poverty, instead of trailing other nations, the U.S. actually comes out on top! He concludes that "when it comes to school improvement, it's poverty not stupid." Poverty causes educational deficiency.
  • or example, Mel Riddile points out that when one conditions on various measures of poverty, instead of trailing other nations, the U.S. actually comes out on top! He concludes that "when it comes to school improvement, it's poverty not stupid." Poverty causes educational deficienc
  •  
    For example, Mel Riddile points out that when one conditions on various measures of poverty, instead of trailing other nations, the U.S. actually comes out on top! He concludes that "when it comes to school improvement, it's poverty not stupid." Poverty causes educational deficiency. Now, I like to actually have data to play around with, in part because people have been known to lie about politically charged issues and in part because I like to have nice graphs (which are not provided by Riddile). Anyway, it turns out that international poverty data is pretty hard to come by and fraught with interpretational difficulties. On the other hand, the National Assessment of Educational Progress provides test data for most of the states in the U.S., and the U.S. Census Bureau provides data on the percentage of people in poverty by state. I took the NAEP data for 8th grade science achievement and regressed on the percentage of people below the poverty line for the measured states. The two are negatively associated: as poverty increases, science achievement scores decrease according to the relationship in the plot below. (Alaska, Kansas, Nebraska, and Vermont did not meet NAEP reporting guidelines and are not included in the plot above.) The association is highly significant (p=9.98*10-6). I also took pilot NAEP data for 8th grade mathematics achievement and regressed on the percentage of people below the poverty line for the measured states. (Evidently, the NAEP has only just started testing for mathematics achievement, and only eleven states were included in their pilot.) Again, the two are negatively associated. The slope of the relation turns out to be almost exactly the same as for science achievement. The association is not as significant, but it is still significant (p=0.0186). (My guess is the association is less significant in this case because fewer states were measured.) Clearly there is an association between poverty and achievement in science and mathem
11More

How Different Types of Knowledge Are Assessed - 0 views

  • Procedural knowledge is knowing how to do something; it involves making discriminations, understanding concepts, and applying rules that govern relationships and often includes motor skills and cognitive strategies
  • Declarative knowledge is knowing that something is the case
  • Problem solving may involve domain-specific strategies, suggesting that different strategies are employed when solving problems in different content a
  • ...6 more annotations...
  • The ability to solve problems builds on declarative knowledge and procedural knowledge.
  • eas, such as math versus writing
  • problem solving involves a sequence of steps, beginning with establishing a representation of the problem, then selecting a strategy that seems appropriate for resolving the problem, followed by evaluating the results of employing that strategy
  • Declarative knowledge involves information one can state verbally. Therefore, tasks will require students to state, explain, discuss, or declare in some other way what they know
  • He described declarative knowledge as a network of propositions, whereas procedural knowledge represented productions. While declarative knowledge involves knowing that something is the case, procedural knowledge involves knowing how to do something
  • To assess problem solving, students are presented a problem to solve or a situation from which they must infer the problem that needs to be solved. Typically, any number of strategies might be used to successfully solve the problem. When scoring student performance where the focus of the assessment is on problem solving, proficiency with particular strategies or other types of procedural (or declarative) knowledge generally is not scored. What is scored are qualities such as the establishment of a clear and appropriate problem representation and sense of goal, the selection of a strategy that is reasonable given the goal to be achieved, and the adequacy with which outcomes from using the selected strategy are evaluated.
  •  
    this item discusses different kinds of knowledge, their connection to Bloom's taxonomy, and how to assess each
  •  
    Different types of knowledge and how to write performance objectives in line with each.
3More

Dan Meyer: Math class needs a makeover | Video on TED.com - 1 views

  •  
    great video on how current math curriculum is set up wrong----great and inspirational MUST USE FOR online and f2f!
  •  
    Dear professor and classmates, Please pardon me for sharing 20+ math links in one clip. I didn't want to share a link and later regret it. so I have been saving and deleting in my private list. I wasn't ready to share until now. Sorry.
  •  
    You are absolutely right!! This was a very inspiration video. I loved how he was able to take the math problems from the book and break it up to make it more engaging.
5More

Why I do what I do | JJ Wagner - 0 views

  • I didn’t like English
    • Donna Angley
       
      We are complete opposites. I love English because I love to write and find it easy to explain why I like something I've read, how it makes me feel emotionally, etc. Writing is as natural as breathing for me. That being said, I don't understand math beyond the basics. Stats was a VERY difficult course for me, and quite frankly if it hadn't been curved I don't think I would have passed. I do understand that math is a lot more concrete; however, it still doesn't make sense to me. Like I always say, everybody is good at something.
  • discussion online.
    • Donna Angley
       
      Try thinking about the posts as small research projects that you share with our class. If you have to respond to a comment, again - think of it as a short research assignment. You're still collaborating, but it will feel less social/personal.
    • Diane Gusa
       
      Hi Jerry, I think the test question is reflective of the discpline. In education and sociology I am looking for application and synthesis of the material. In math I think doing the problem is like a math essay, is it not? I hate that my grandson, gifted in math (he would convert fractions in his head at age 4) but he is only feed in school on repetitive worksheets on computation...any suggestions what I can do this summer to feed his gift? Diane
7More

LD OnLine :: Technology-Supported Math Instruction for Students with Disabilities: Two ... - 0 views

  • One kind of cognitive task that can be offloaded to a computer is converting text, symbols, and mathematical notations. These tools can support students who have difficulty decoding text and symbols
  • Too often, special education students study mathematics by first learning isolated skills. Then they apply these skills by solving narrowly defined math problems that are purported to provide practice for these skills. Unfortunately, this strategy often leads to the practice of rote procedural skills
  • inert knowledge
  • ...3 more annotations...
  • students may have the mathematical knowledge and procedures they need but may be unable to use them because they lack the conceptual understanding that allows them to match their knowledge to the problem situation
  • anchored instruction
  • declarative, procedural, and conceptual.
  •  
    LD strategies for math education
4More

Adaptive Learning System - The Role of Adaptive Learning in Math - 0 views

  • Pedagogically and research-based intelligent adaptive learning technology accesses and stays in the Zone of Proximal Development (ZPD) for each learner. That means it provides the right next lesson at the right level of difficulty at the right time. When work is easy, learners can do the work on their own without any help. It’s in their "comfort zone." If all the work a learner is asked to do is always in the comfort zone, no real learning will take place and the learner will eventually lose interest. Conversely, when the work is too hard, the learner becomes frustrated and will likely give up. The area between the comfort zone and the frustration zone is the one where true learning will take place – the optimal learning zone. It’s the area where a learner will need some help or will need to work hard to understand a concept or complete a task. By keeping the challenge appropriate, the learner is guided to be a mathematical ‘doer’ — someone who thinks and strategizes in ways they can apply in school and in their real life experience. This is optimal teaching and optimal learning.
    • lkryder
       
      This has been my thinking all along on the gamefying and my weekly really hard quizzes. Now I hope to build on it.
  •  
    This is a page offering a product BUT what I found fascinating was their use of ZPD as the learning opportunity in adaptive technologies. I recall as a child having programmed learning guides that I loved and I did them for hours ( I recall they were about logic and problem solving- very cool). They were printed in a book. Now that kind of thing is frowned upon as low on Bloom but all the publishers are creating these adaptive supplements and students love them.
  •  
    This is a page offering a product BUT what I found fascinating was their use of ZPD as the learning opportunity in adaptive technologies. I recall as a child having programmed learning guides that I loved and I did them for hours ( I recall they were about logic and problem solving- very cool). They were printed in a book. Now that kind of thing is frowned upon as low on Bloom but all the publishers are creating these adaptive supplements and students love them.
9More

Using Technology to Enhance Engaged Learning for At-Risk Students - 1 views

  • Teachers can draw on technology applications to simulate real-world environments and create actual environments for experimentation, so that students can carry out authentic tasks as real workers would, explore new terrains, meet people of different cultures, and use a variety of tools to gather information and solve problems." (p. 43)
  • technology can enhance student engagement and productivity. More specifically, technology increases the complexity of the tasks that students can perform successfully, raises student motivation, and leads to changes in classroom roles and organization
  • collaborative.
  • ...5 more annotations...
  • meaningful, engaged learning.
  • authentic tasks.
  • the intersection of learning and technology,
  • monitor and document each student's progress.
    • Melissa Pietricola
       
      This is what I am currently wrestling with: how do I monitor student contributions to my course if they work in a cooperative group? I hated being that kid in the group that did all the work!
  •  
    "Teachers can draw on technology applications to simulate real-world environments and create actual environments for experimentation, so that students can carry out authentic tasks as real workers would, explore new terrains, meet people of different cultures, and use a variety of tools to gather information and solve problems."
9More

Metacognition: An Overview - 1 views

  • Metacognitive experiences involve the use of metacognitive strategies or metacognitive regulation (Brown, 1987). Metacognitive strategies are sequential processes that one uses to control cognitive activities, and to ensure that a cognitive goal (e.g., understanding a text) has been met. These processes help to regulate and oversee learning, and consist of planning and monitoring cognitive activities, as well as checking the outcomes of those activities.
  • Self-questioning is a common metacognitive comprehension monitoring strategy. If she finds that she cannot answer her own questions, or that she does not understand the material discussed, she must then determine what needs to be done to ensure that she meets the cognitive goal of understanding the text.
  • Knowledge is considered to be metacognitive if it is actively used in a strategic manner to ensure that a goal is met. For example, a student may use knowledge in planning how to approach a math exam: "I know that I (person variable) have difficulty with word problems (task variable), so I will answer the computational problems first and save the word problems for last (strategy variable)." Simply possessing knowledge about one's cognitive strengths or weaknesses and the nature of the task without actively utilizing this information to oversee learning is not metacognitive.
  • ...5 more annotations...
  • Cognitive Strategy Instruction (CSI) is an instructional approach which emphasizes the development of thinking skills and processes as a means to enhance learning. The objective of CSI is to enable all students to become more strategic, self-reliant, flexible, and productive in their learning endeavors (Scheid, 1993). CSI is based on the assumption that there are identifiable cognitive strategies, previously believed to be utilized by only the best and the brightest students, which can be taught to most students (Halpern, 1996). Use of these strategies have been associated with successful learning (Borkowski, Carr, & Pressley, 1987; Garner, 1990).
  • Metacognition enables students to benefit from instruction (Carr, Kurtz, Schneider, Turner & Borkowski, 1989; Van Zile-Tamsen, 1996) and influences the use and maintenance of cognitive strategies.
  • Metacognition and Cognitive Strategy Instruction
  • The study of metacognition has provided educational psychologists with insight about the cognitive processes involved in learning and what differentiates successful students from their less successful peers. It also holds several implications for instructional interventions, such as teaching students how to be more aware of their learning processes and products as well as how to regulate those processes for more effective learning.
  • Metacognition refers to higher order thinking which involves active control over the cognitive processes engaged in learning. Activities such as planning how to approach a given learning task, monitoring comprehension, and evaluating progress toward the completion of a task are metacognitive in nature. Because metacognition plays a critical role in successful learning, it is important to study metacognitive activity and development to determine how students can be taught to better apply their cognitive resources through metacognitive control.
  •  
    metacognition
2More

http://www.sci.uidaho.edu/polya/math144/video_instruction/video_instruction.htm - 0 views

  •  
    NOTE TO SELF: CONTACT IT SUPPORT TO DOWNLOAD REAL PLAYER ON MY LAPTOP!
  •  
    Joan, I love this note to self! I have this problem all the time with my work computers and it is so frustrating. Just wanted you to know that I feel your pain!
5More

CL-1: Field-tested Learning Assessment Guide (FLAG): Assessment Primer (1 of 5) - 0 views

  • There is considerable evidence showing that assessment drives student learning. More than anything else, our assessment tools tell students what we consider to be important. They will learn what we guide them to learn through our assessments.
    • lkryder
       
      If you begin a course design with this in mind, and fold your feedback loops in carefully, students will know what matters and what to work at for success
  • Assessment is more than grades To many, the word "assessment" simply means the process by which we assign students grades. Assessment is much more than this, however. Assessment is a mechanism for providing instructors with data for improving their teaching methods and for guiding and motivating students to be actively involved in their own learning. As such, assessment provides important feedback to both instructors and students. Assessment is Feedback for Both Instructors and Students Assessment gives us essential information about what our students are learning and about the extent to which we are meeting our teaching goals. But the true power of assessment comes in also using it to give feedback to our students. Improving the quality of learning in our courses involves not just determining to what extent students have mastered course content at the end of the course; improving the quality of learning also involves determining to what extent students are mastering content throughout the course.
  • Assessment Drives Student Learning The types of assessment usually performed in first-year science, math, engineering, and technology (STEM) courses--giving students tests--merely inform students about their grade, or ranking, after they have received instruction. In addition, these common testing techniques--which typically test for fact-based knowledge and algorithmic problem solving--tell our students that this is the type of knowledge we think is most important. That is, we appear to value the understanding of concepts at a relatively low level. Given that this is the type of assessment our students most frequently encounter, and that it will eventually lead to their final course grades, students learn to study the content in our courses in an expeditious way that allows them to succeed in passing many first-year STEM courses without necessarily developing deep understanding of concepts. It is our assessment that drives students learning.
  •  
    The full primer for convenience
10More

Education World ® Administrators Center: Making Retention A Last Resort - 0 views

  • Retaining students while their peers are promoted is bad for a child's self-esteem and may not help them academically, according to the argument. But promoting children without the skills for the next grade can be just as demoralizing.
  • "Multi-age learning is the gift of time," Jetel told Education World. "Students work to complete a curriculum cycle. The activities are open-ended and students can work on at their own pace."
  • on Student Grade Retention and Social Promotion, the National Association of School Psychologists (NASP) notes that the use of grade retention has increased over the past 25 years, despite little indication of its effectiveness.
  • ...6 more annotations...
  • between 30 percent and 50 percent of students in the U.S. are retained at least once before ninth grade.
  • The results showed that grade retention had a negative impact on all areas of achievement, including reading, mathematics, and language, as well as socio-emotional adjustment, such as peer relationships, self esteem, problem behaviors, and attendance
  • implementing multiple support programs to help students stay on track to pass the tests the first time
  • students who need extra help will receive differentiated instruction from teachers trained to meet their needs. Students also will receive instruction before and after school, on weekends, and during a Summer Success Academy, designed for second and third graders. The academy's focus will be on reading, writing, and math, and classes with no more than 15 students, according to Klein.
  • smaller classes and earlier support services
  • 'What didn't work? What wasn't done earlier? What do we do to identify the difficulties a kid is having?' If you can't answer the question why the student didn't learn, you are in danger of repeating mistakes."
  •  
    Social Retentions and the risks to the students
1 - 16 of 16
Showing 20 items per page