Teaching Math, Science, and Technology in Schools Today: Guidelines for Engaging Both Eager and Reluctant Learners (2nd Edition)
Notes from the Preface
Having a negative attitude toward certain content is bound to have a similar negative impact on students (v).
Learning math, science, and technology is compared by Montreal teacher Eugen Pascu to learning to drive a car: "First you've got to memorize the rules of the road. Then you've got to apply them to get behind the wheel and actually move the car....You need to learn formulas but you also have to understand how they work. Learn the rules, then see how the rules work (Pertiz, 2013). (v)
Questions, engagement, and curiosity are viewed as natural partners for mathematical problem solving, scientific inquiry, and technology-rich learning. With teacher assistance, even students who are having learning problems can move from believing they "can't do" or "don't like" these subjects to having a sense of genuine achievement and confidence (vii).
In the workd outside of school, creative and collaborative engagement is central to mathematical problem solving, scientific inquiry, and technological innovation. So why not use a similar approach for all students in K-8 classrooms? (Vii)
Chapter 1: Helping All Students Learn About Math and Science
The Common Core State Standards recognize the need for changing societal attitudes toward numeracy and literacy. They also suggest that in a wired world, students of all ages need to learn about previously understated dimensions of math and science (CCSS, 2013). (1)
In spite of their obvious importance, math and science are just about the only topics for which more than a few well-educated adults will freely admit ignorance. Teachers reflect the general population. So it is little wonder than when it comes to teaching these subjects, many of the characteristics of effective instructions fall by the wayside (2).
When teaching math and science, asking disaffected learners to reason, solve problems, and maintain a positive disposition may be a tall order. So we should not be surprised when teachers sometimes pay more attention to procedural knowledge than they do to reflection and understanding (2).
In spite of the difficulties, the primary goal of instruction should be getting every student in the classroom to develop and use the higher-level thinking skills associated with problems solving and inquiry (2).
Math and Science Instruction for All Students
Identifying some reasons behind the reluctance to learn math and science is essential if we are going to engage student interest and help them succeed. The key is finding something that will spark every student's interest. The next step is turning that spark into a flame (3).
Everyone Needs to Understand Math and Science
The need to understand math and science in everyday life has never been greater...Data enhanced decisions are ore than ever part of human decision making. Statisticians and data analysts pay more attention to correlations than human predispositions (Mayer-Schonberger and Culier, 2013). (5)
Effective use of visuals, manipulatives, and learning aids often help overcome various problems. Working in pairs or small groups is a good motivators. Peer involvement expands and strengthens language skills and increases students' confidence.
When students fail to see the connections among concepts, math and science become a rote exercise, and understanding is limited. As experienced teachers will tell you, simply memorizing terms without knowing what they mean is not useful. Comprehension is the goal (8).
Many struggling students do not understand that being successful in math and science involved employing problem-solving strategies. Teachers have to teach them how to be metacognitive learners and help them recognize the thinking strategies they are using. Metacognition strategies can amplify self-reliance and creativity for struggling learners. Teachers who model thoughtfulness and encourage students to go a long way toward fully engaging struggling students (8-9).
Collaborative Inquiry in Math and Science
All students can flourish when good teaching is combined with collaborative inquiry and an engaging curriculum (Tomlinson and Imbeau, 2010). Collaborative inquiry is a form of reasoning and peer cooperation that begins with a problem and ends with a solution. It generally involves asking questions, observing, examining information, investigating, arriving at answers, and communicating the results. (9)
A collaborative inquiry approach to the teaching of math and science has been found to work well with struggling learners. Among other things, it helps these students experience the excitement of mathematics and science activities in learning groups (9).
Knowledge of math and science has always been constructed in association with others. At all levels mathematical and scientific inquiry is much more than an individual endeavor. So it is best if elementary and middle school students employ procedures similar to the collaborative procedures that mathematicians and scientists actually use when they work.
The collaborative inquiry approach is a student-centered process of cooperative discovery. The teacher often gives the students directions and materials--but does not tell the small group exactly how to go about doing their work. The teacher encourages conversation and provides activities that help students understand how math and science are applies in the world outside of the school. The teacher might also give a brief-whole class presentation and then move from small group to small group, encouraging questions and guiding student observations (10).
Collaboration, Inquiry, and Reluctant Learners
Inquiry is sometimes thought of as the way people study the world and propose explanations based on the evidence they have accumulated. It involves actively seeking information, truth, and knowledge. When collaboration is added to the process, it helps build the positive relationships that are at the heart of the learning community.
Collaborative inquiry may be thought of as a range of concepts and techniques for enhancing interactive questioning, investigation, and learning. When questions that connect to student student experiences are raised collectively, ideas and strengths are shared in a manner that supports the struggling students' search for understanding (Snow, 2005). (11)
Science classes will do Collaborative seed example on pages 12-13
Making Instructional Decisions with Differentiated Learning
Differentiated learning is an organized approach through which teachers and students work together in planning, setting goals, and monitoring progress. In such classrooms, the teacher draws on the cultural knowledge of student by using culturally and personally relevant examples. They show great respect for learners by valuing their similarities and differences, not by treating everybody the same (13).
The most useful teaching approach for the struggling learner is often well-organized differentiated instruction (Tomlinson and Cunningham Eidson, 2003). A teacher who is organized examines the conditions surrounding the child such as curriculum content, the classroom environment, and the student's academic and social behaviors. The ways students react to information and respond to feedback are also important....But teachers know that no approach is effective in every situation, so it is important to be flexible.
Discovering Ways to Differentiate Instruction
What is clear is that struggling students seem to have have the hardest time with the traditional classroom setting (straight desks, teacher lectures, textbooks, worksheets, lots of listening, waiting, following directions, reading, and writing.) In other environments, students who struggle have much less difficulty, for example in an art classroom, a wood shop, a dance floor, or the outdoors. In these differentiated classroom settings where students have opportunities to engage in movement, hands-on learning, and other new learning approaches, their interest and desire to learn have been shown to be at or above average (Gardner, 1993).(15)
Meeting the Principles and Standards
Equity: High-quality math and science require raising expectations for students' learning. All students must have opportunities to study and learn mathematics and science. This does not mean that every student should receive identical instruction: indeed, it demands that appropriate accommodations be made for all students. Resources and classroom supplies are also a large part of equity (17).
Curriculum: coherent, focused on math and science, and articulated across grade levels....building deeper understandings provides a map for guiding teachers through the different levels of learning.
Technology: Tools such as calculators and computers provide visual images of math and science ideas. They facilitate learning by organizing and analyzing data, and they compute accurately.
Assessment: Assessment should support the learning of math and science and provide useful information to students and teachers.
Teaching: Effective teachers understand mathematics and science, comprehend what underachieving students know and need to learn, and challenge and support them through learning experiences. Teachers need to know multiple kinds of knowledge: knowledge of the subject, pedagogical knowledge, and an understanding of how children learn. Different techniques and instructional materials also affect how well their students learn mathematics and science. Struggling learners are often inundated with only practice materials to help them master the "basic skills."They quite often lack the conceptual procedures of real understanding. Students frequently forget procedures and are referred back to the same uninteresting skill-based drill work. The learner is not the focus rather the basic skill drill is the center of attention (17).
Learning: Math and science must be learned with understanding. Students actively build new knowledge from prior experience. Students should have the ability to use knowledge in a flexible manner, applying what is learned, and melding factual knowledge with conceptual understanding
Struggling Learners and the Math and Science Standards
If students can't learn the way we teach, we must teach them the way they learn.
-- Carol Ann Tomlinson
We want all students, particularly struggling learners, to be involved in high-quality engaging mathematics and science instruction. High expectations should be set for all, with accommodations for those who need them (18). The National Council of Teachers of Mathematics and the National Science Foundation have developed standards that serve as guides for focused and enduring efforts to improve students' school mathematics and science education. These content standards provide a comprehensive set of standards for teaching mathematics and science from kindergarten through grade 12 (18). (See overview in NTCM (2000), and NGSS (2013).
Going Beyond Skill Mastery
Students who complete their math and science lessons with little understanding quickly forget of confuse the procedures. Understanding important ideas and accurately completing problems are some of the first steps in becoming mathematically and scientifically skillful. Mathematics and science contains five strands of thought:
1. Understanding ideas and being able to comprehend important content.
2. Being flexible and using accurate procedures.
3. Poising and solving problems.
4. Reflecting and evaluating knowledge.
5. Reasoning and making sense and value out of what is learner. (20)
Organizing Successful Lessons
Stage 1: Review: access prior knowledge--make connections between familiar and new information
Stage 2: Demonstrate skill or knowledge- increase student engagement and promote independent student activities
Stage 3: Guided practice- reinforce language skills, partner, and share. Do a variety of problems.
Stage 4: Check for Understanding and provide feedback--summarize strategies and evaluate
Teacher provides continuous feedback at each stage so that errors can be found and corrected (21-22).
Summary, Conclusion and Looking Ahead:
At every age level, it is important to think big and risk failure to make new ideas and positive change possible. It does not have to happen at once---teachers can think big and start small as they weave new ideas into the educational fabric (26).
When it comes to student learning, there is no substitute for a good teacher who develops lessons that combine thinking and feeling in a way that reaches both the head and the heart (28).
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