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Product of Learning
Transcript of Product of Learning
Students don't fully understand the concepts that surround this topic
Usually memorize facts
Large part of EOC
Logarithms are a completely new concept Conclusions:
Effects of guess-and-check problems
Discovery lessons that didn't seem like they were teaching themselves
Applications are useful
Warm-ups Teacher Themes:
Frustrated with discovery lessons
Enjoyed & needed group work
Discourse! What Does the Literature Say?
Applications are more effective if they are relevant to the real world
Discovery learning helps students think originally, encourages team work, and learn new approaches
Logarithms can easily be connected to exponents to develop an appreciation of their meaning
Exponential and Logarithmic functions and their relevance throughout NCSCS, Common Core and NCTM's Principles and Standards for School Mathematics Student Themes:
Dislike of "teaching themselves"
Like doing "fun" activities
Learn from hands-on activities
Enjoyed daily warm-up Most liked: M&M Lab, Project, Drug Filtering Lab
Least liked: Project, Finding e Emphases:
Motivating the existence of logarithms Goal:
Design activities that will help students become more proficient with exponential and logarithmic functions in order to deepen and clarify their understanding. 1. Million dollars or penny doubled each day; A Grain of Rice
2. Drug Filtering Lab; growth and decay word problems
3. M&M Lab
4. Quiz; Euler's number; continuously compounded
5. Log a what?
6. Quiz; discover properties of logarithms
7. More properties; exponential equations
8. Logarithmic equations
9. Equations practice - traditional & applications
12 & 13. Present projects "I like it better when you teach the lessons. I got next to nowhere today."
"The M&M Lab was fun. It was cool to see and count our own data."
"I liked today's lesson because we had a fun, hands-on experience messing with the M&Ms. It helped us to do math better because we had something to look forward to afterwards."
"Real-world problems help keep me focused and I really like this method of teaching." "Inquiry-based lessons were a struggle because it is not how they are used to class being conducted."
"It was the discrepancy in answers that brought about the true group work."
"I found the students not only discussing their answers and how they arrived at them, but participating in general conversations about life." "An ultimate goal of mathematics teaching is to prepare young people to function knowledgeably and confidently in real-world problem-solving situations. Mathematical modeling is a paramount form or real-world problem solving." "Learning through discovery has been one of the cornerstones of mathematics education theory for many years." "In making logarithms more impressive and to give the student a fuller conception of their real meaning the first thing to be considered and continually stressed throughout the study of logarithms is that the logarithm of a number is really the power to which the base is raised to the given number." 1.01 Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems. NCSCS
2.03 Use exponential functions to model and solve problems; justify results. NCSCS
2.04 Create and use best-fit mathematical models of linear, exponential and quadratic functions to solve problems involving sets of data. NCSCS
Understand and compare the properties of classes of exponential and logarithmic functions. NCTM PSSM
Identify essential quantitative relations in a situation and determine the class or classes of functions that might model the relationships. NCTM PSSM
F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. CCSSM
F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. CCSSM
F-LE.4 For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards (*). CCSSM Methodology:
Reflections What now?
How I'll teach this unit in the future
How I'll change/adjust my teaching style
What this POL taught me Student Reflections
Completed at the end of each class throughout the unit
Read multiple times to look for themes
Completed at the end of each school day throughout the unit
Read multiple times to look for themes Harper, J.P. (1942). Teaching logarithms. The Mathematics Teacher, 35, 217 – 221. Chissick, N. (2004). Learning through inquiry. The Mathematics Teacher, 91, 6 – 11. Swetz, F. (1989). When and how can we use modeling?. The Mathematics Teacher, 82, 722 – 726.