Assessment seems to have a completely different effect on students' attitudes based on whether they frequently pass or frequently fail.
Students who demonstrate winning streaks are confident and hopeful, demonstrate continual evidence of success, and are excited to learn. These students are likely to seek more feedback and more challenges. On the other hand, students who demonstrate losing streaks are frequently hopeless and give up easily. They do not feel safe at school and feel that they are always being evaluated. They see feedback as criticism and do not seek challenges or new ideas. Stiggins tries to eliminate this gap.
Rather than using assessment to sort students into winners and losers based on performance, educators should use assessment to help student learn. Stiggins offers an alternative notion, Assessment For Learning (as opposed to assessment of learning). This alternative encourages teachers to turn assessment into a process that involves sharing goals and targets with students, provide frequent and continual feedback in student-friendly language, and provide examples of outstanding student work. This causes students to self-assess and notice trends in their own achievement. Students become more aware of their academic progress. They begin to understand what is expected and make decisions on how to become better. They also generate their own feedback and set their own goals. The hope, Stiggins says, is not to eliminate failure but to eliminate losing streaks. This helps boost student confidence and motivates them to try more.
References
Stiggins, R. (). Assessment through the student's eyes. Educational Leadership, 64(8), 22–26.
Chapter 3: Learning and Knowledge in the Twenty-first Century
To be completely honest, I thought the article was just short of a textbook. I remember reading about different perspectives of educational psychology in another course, and much of the article was information that could have been left out. A few of the topics deviated from (what I understood to be) the original thesis of the article, which was about how technology is changing learning and teaching in this day and age.
I enjoyed the introduction of the article because it compared different beliefs and views on learning from very different time periods, while relating back to the theme of technology. It seemed as if educators of the late 19th century were preparing their students for the specific jobs they thought they would have. Whereas now, students seem to be more well-rounded. In the past, school was seen as a means to an end, but now, school is seen as preparation for more learning in the future. One thing that prepares young learners today is that they really do learn how to learn with technology. Views on learning nowadays emphasize cognitive processes like critical thinking, problem solving, and decision making over lower arithmetic and computational skills.
A few big questions did come across my mind while I was reading about this. At what point do we draw the line? Students don't need to be able to take the cube root or write the prime factorization of very large numbers anymore, so why should they need to be able to compute the limit of a rational function or find the general solution of a first order non-linear differential equation? At what point do we say, “That's enough, the calculator can do the rest.”? Why are we, as educators, so selective about what we decide students ‘should’ know?
Aside from discussing the differences due to technology of learning beliefs across time, the article also discussed different perspectives on learning. The Behavioral perspective (Skinner) focuses on external, observable responses. Drill and practice are reinforcements for learning, and educational technology can be highly effective (unless it is excessive or premature, etc.). Behaviorists state that learning is sequential and hierarchical, such as an axiomatic system.
Cognitive psychologists (Piaget) accept that learning is a result of adaptation motivated by disequilibrium. Learners apply existing schema to change what they know about new information, but also alter existing schema to fit new information. This push-and-pull balance of assimilation and accommodation is required when transferring from disequilibrium to equilibrium, thus satisfying the learner's drive. Cognitivists also support scaffolding, which requires teachers to guide and assist learners. Through scaffolding, teachers can determine what type of help to offer and when and how to offer it. Discourse is encouraged so that teachers will be able to recognize students' Zones of Proximal Development, the zone in which the transfer from disequilibrium to equilibrium is most effective, and keep them right in that zone to maximize learning. Before the ZPD, students are unchallenged and bored, while after the ZPD, students are intimidated and discouraged.
Constructivists say that teachers should create complex and realistic learning environments, encourage social interaction and communication, present multiple and diverse perspectives and representations, and facilitate student ownership in learning. Researchers today are emphasizing learning environments that take a mix of all three perspectives. Instruction should be student-centered, multisensory and multimedia-involved, collaborative as well as competitive, active and exploratory, critical, logical, and both theoretical as well as practical.
References
Niess, M. L., Lee, J. K., & Kajder, S. B. (). Guiding learning with technology. Hoboken, NJ: John Wiley & Sons, Inc.
The article on using a Computer Algebra System for teaching mathematics had several major points. The introduction was about how CAS changes teaching and learning of math. In a classroom where students are using CAS, the topics, focus within topics, and goals of lessons will change. Lessons are no longer algorithmic but focus on using operations to understand meaning. The article also mentioned two goals for teaching: to develop theory of mathematical concepts, and to use mathematical concepts in real-world models and applications. Teachers should try to construct exam questions to meet these goals. There were two schemes for analyzing exam questions.
The first scheme was based on testing skills and abilities of students, and took a more educational approach. It measured the educational value of problems as questions on an exam. The educational scheme had five categories.
The CAS-Insensitive Questions did not make very much use of the CAS, and computation plays a minor role.
The Questions Changing with Technology made a big difference once the CAS was introduced because time needed to solve the problem was greatly reduced.
The Questions Devalued with CAS involved rare tricks and hard-to-remember equations to solve, so the CAS appeared insignificant.
The Questions Testing Basics became trivial when using CAS because the answer would be produced immediately; however, the student needed knowledge about syntactical structure.
The last category, Rediscovered Questions, are geared to support creativity, fluency, and flexibility, but are rare because of the difficulties in evaluating and grading.
The second scheme was based on the usefulness of CAS and took a rather technical approach. It measured the role of technology for answering a question. The technical scheme also had five categories, grouped into how significant CAS was in solving the problem, and how well the student should be familiar with CAS.
In terms of significance, Primary Use needed CAS as a major activity,
while Secondary Use did not facilitate CAS as strongly.
Regarding familiarization, Advanced Use required in-depth knowledge of CAS,
while superficial knowledge of CAS suffices for Routine Use.
CAS is of very little help for questions in the last category, No CAS Use.
After discussing different types of problems in different categories, the article compared the two and made some observations about CAS. It facilitates the two teaching goals discussed above, it reveals educational value of exam questions, forces teacher to be conscious about exam questions, and revives the “forgotten” questions. When choosing exam questions, teachers need to keep the aforementioned goals in mind, but also question how they test the student. Exam questions should test general abilities rather than computational skills. In any testing environment the act of understanding and the act of overcoming an obstacle are equally important in the learning process. In addition, intellectual concentration and emotional tension are present and culminating, which creates a learning situation per se.
References
Kokol-Voljc, V. (year unknown). Exam questions when using CAS for school mathematics teaching. publication unknown.
