QUT Mathematical Sciences Seminar series, November 1 2013
Traditionally at QUT, mathematics and statistics are taught using a face-to-face lecture/tutorial model involving large lecture classes for around 1/2 to 3/4 of the time and smaller group tutorials for the remainder of the time. This is also one of the main models for teaching at other campus-based institutions. Recently, in response to (learning) technology advances and changes in the ways learners seek education, QUT has made a significant commitment to a “Digital Transformation” project across the university. In this seminar I will present a technical overview, with some demonstrations, of a pilot project that seeks to investigate how digital transformation might work in a QUT mathematics or statistics subject. In particular, I will discuss the use of tablet PC technology and specialist software to produce video learning packages. This approach has been trialled in a transition level mathematics unit this semester. I will also cover integration of these learning packages with QUTs Learning Management System “Blackboard”. This seminar is a technical preview to another talk I will give early in the new year that will look at the impact of the altered learning experience on student outcomes, feedback and the unit itself.
Math Resources! Problems, tasks, strategies, and pedagogy. An hour of my 90-min session on math task design at Cal Poly Pomona for a group of teachers (mainly elementary school).
This document discusses key elements of effective mathematics lessons and tasks. It outlines characteristics of high-quality tasks such as incorporating multiple representations, strategies, solutions, and entry points to promote critical thinking. It emphasizes the importance of tasks connecting mathematical concepts and requiring cognitive demand. Questions should probe student thinking or push their understanding. Lessons should build in opportunities for students to communicate their evolving understanding. The document provides examples of effective tasks and questions to further student learning.
- The document discusses research on mathematics education in the United States, finding that only about a third of students are proficient in math based on national assessments. It also discusses research showing US students performing poorly compared to other nations.
- The research emphasizes the need for a well-designed curriculum, quality teacher preparation, and explicitly teaching concepts and making connections to help students succeed in algebra and beyond. It discusses characteristics of students with learning difficulties in math.
- The document provides an overview of effective teaching practices informed by research, including concrete-representational-abstract instruction, explicit teaching, sequencing skills appropriately, and providing cumulative practice and review.
Have you ever dreamed of teaching a pre-calculus level course where the algebraic manipulation is de-emphasized and the emphasis is shifted to conceptual understanding and practical skills that directly apply to transfer classes? Learn how your wishes can come true by making simple changes around curriculum, pedagogy, and technology.
The document discusses issues with how fractions are currently taught in US schools and recommends improvements. It notes that students struggle with fractions and this hinders later success in algebra. A presidential panel recommends schools focus more on mastering the basics like fractions, in addition to geometry. It emphasizes fractions are a major obstacle and schools should teach them in a more in-depth way.
The document discusses differences between how American and Chinese teachers approach teaching elementary math concepts. It analyzes teacher responses to sample math problems involving subtraction, multiplication, and division of fractions. American teachers tended to focus on procedures and memorization, while Chinese teachers emphasized mathematical structure and developing conceptual understanding. The document advocates for teaching math in a way that builds students' number sense and understanding of mathematical concepts and properties.
The document summarizes a teacher's lesson on the concepts of definite and indefinite integrals in calculus. The teacher used screencasting to flip the classroom, allowing students to watch video lessons before class. In class, the teacher used whiteboarding to have students work through sample problems in small groups, then present their solutions. The teacher addressed common student misconceptions about forgetting the "+C" constant when taking antiderivatives by having students solve practice problems set to music. Understanding these integral concepts is crucial for students' subsequent calculus learning.
The document discusses introducing random slopes to multilevel models. Random slopes allow the relationship between a predictor variable (like tutor hours) to vary across levels (like schools). This accounts for differences in how effective an intervention may be depending on context. The notation for random slopes models is presented, with classroom and student models nested within school-level models. Implementing random slopes helps address non-independence of observations and better estimate variability.
Math Resources! Problems, tasks, strategies, and pedagogy. An hour of my 90-min session on math task design at Cal Poly Pomona for a group of teachers (mainly elementary school).
This document discusses key elements of effective mathematics lessons and tasks. It outlines characteristics of high-quality tasks such as incorporating multiple representations, strategies, solutions, and entry points to promote critical thinking. It emphasizes the importance of tasks connecting mathematical concepts and requiring cognitive demand. Questions should probe student thinking or push their understanding. Lessons should build in opportunities for students to communicate their evolving understanding. The document provides examples of effective tasks and questions to further student learning.
- The document discusses research on mathematics education in the United States, finding that only about a third of students are proficient in math based on national assessments. It also discusses research showing US students performing poorly compared to other nations.
- The research emphasizes the need for a well-designed curriculum, quality teacher preparation, and explicitly teaching concepts and making connections to help students succeed in algebra and beyond. It discusses characteristics of students with learning difficulties in math.
- The document provides an overview of effective teaching practices informed by research, including concrete-representational-abstract instruction, explicit teaching, sequencing skills appropriately, and providing cumulative practice and review.
Have you ever dreamed of teaching a pre-calculus level course where the algebraic manipulation is de-emphasized and the emphasis is shifted to conceptual understanding and practical skills that directly apply to transfer classes? Learn how your wishes can come true by making simple changes around curriculum, pedagogy, and technology.
The document discusses issues with how fractions are currently taught in US schools and recommends improvements. It notes that students struggle with fractions and this hinders later success in algebra. A presidential panel recommends schools focus more on mastering the basics like fractions, in addition to geometry. It emphasizes fractions are a major obstacle and schools should teach them in a more in-depth way.
The document discusses differences between how American and Chinese teachers approach teaching elementary math concepts. It analyzes teacher responses to sample math problems involving subtraction, multiplication, and division of fractions. American teachers tended to focus on procedures and memorization, while Chinese teachers emphasized mathematical structure and developing conceptual understanding. The document advocates for teaching math in a way that builds students' number sense and understanding of mathematical concepts and properties.
The document summarizes a teacher's lesson on the concepts of definite and indefinite integrals in calculus. The teacher used screencasting to flip the classroom, allowing students to watch video lessons before class. In class, the teacher used whiteboarding to have students work through sample problems in small groups, then present their solutions. The teacher addressed common student misconceptions about forgetting the "+C" constant when taking antiderivatives by having students solve practice problems set to music. Understanding these integral concepts is crucial for students' subsequent calculus learning.
The document discusses introducing random slopes to multilevel models. Random slopes allow the relationship between a predictor variable (like tutor hours) to vary across levels (like schools). This accounts for differences in how effective an intervention may be depending on context. The notation for random slopes models is presented, with classroom and student models nested within school-level models. Implementing random slopes helps address non-independence of observations and better estimate variability.
JiTT - Blended Learning Across the Academy - Teaching Prof. Tech - Oct 2015Jeff Loats
This document summarizes a presentation on implementing Just-in-Time Teaching (JiTT), a blended learning strategy. The presentation provides an overview of JiTT, shares data from courses that have used JiTT showing increased student preparation and performance, and offers recommendations for getting started with JiTT. Sample JiTT questions are also presented along with student responses to demonstrate how the strategy works.
Ace Maths Unit Two: Developing Understanding in Mathematics (PDF)PiLNAfrica
In this unit, the theoretical basis for teaching mathematics – constructivism – is explored. Varieties of teaching strategies based on constructivist understandings of how learning best takes place are described
This document provides an overview of a webinar for fifth grade teachers on the CCGPS unit for order of operations and whole numbers. The webinar will focus on the big ideas, standards, and resources for the unit. Teachers will learn about navigating a CCGPS unit, new aspects of the frameworks, and strategies for developing students' number sense. They will also discuss tools for teaching number operations and developing mathematical understanding.
An Intelligent Microworld as an Alternative Way to Learn Algebraic ThinkingCITE
This document summarizes a research project that designed and tested an online environment called eXpresser to help students learn algebraic thinking and mathematical generalization. The project involved:
1) Developing eXpresser as an interactive microworld for building patterns and expressing rules that govern the patterns.
2) Conducting design experiments with 11-12 year old students to test eXpresser and gather feedback.
3) Interviewing students and finding that eXpresser helped them articulate relationships between quantities in patterns and validate rules through animation.
4) Designing group tasks for students to share and compare patterns/rules, finding most could determine if rules were equivalent.
This document provides resources for teaching fractions to 3rd grade students using technology. It includes rationales for integrating technology, such as enhancing lessons and student understanding through visuals. The document then summarizes various online resources like blogs, videos, games and worksheets that can be used for fraction instruction and practice. These resources allow students to learn fractions interactively in order to build their skills in a fun and engaging way.
The document provides an overview of the Common Core State Standards including the goals, adoption by states, instructional shifts, implementation timeline, and assessments. It discusses narrowing the standards to focus more deeply on key concepts, building coherence across grade levels, and requiring equal rigor in conceptual understanding, skills, and application. Sample 5th grade math standards on fractions and diagrams are presented. The document emphasizes how the standards complement other initiatives to prepare students for college and careers.
This webinar provided an overview of the 4th grade CCGPS mathematics unit on whole numbers, place value, and rounding in computation. The big idea of the unit is to deepen understanding of place value and its usefulness in estimation and computation. Resources were shared for exploring strategies for teaching key concepts like multi-digit multiplication and comparing fractions. Feedback was requested to help improve future unit-by-unit webinars. Participants were also encouraged to join a wiki for ongoing discussion of CCGPS mathematics.
The document discusses a workshop on engineering mathematics course planning at Alpha College of Engineering. It covers important educational goals of promoting retention and transfer of learning. It discusses different types of learning - rote learning which focuses on knowledge acquisition, and meaningful learning which provides students with knowledge and cognitive processes for problem solving. The course plan details topics to be covered each semester including classifying topics into remembering, understanding and applying categories. It also discusses assessing students for retention and transfer of learning goals.
Use of Technology in Education, But at What Cost?IJITE
Use of technology in the field of education has been a blessing. Faster grading, quicker notes / media availability for students, interactive communication outside of classrooms with students and faculty, online courses etc. have added to the enhancement of our education system. But when technology is pushed in teaching without proper thought, it becomes a black box approach at the cost of intuition, commonsense, and overall understanding of the concepts. Instead of supplementing technology in the process of learning, it has been used in making the black box approach more common. When we can shift the question from “How to educate with technology?” to “How to teach people best, and how should we design learning experiences in light of existing technology?”, then learning becomes a way to quench curiosity, and passion for learning will become a never ending pursuit for students. Models and textbook theories can help build the knowledge base, but they miss the context [5,7]. Students take them at face value without thinking through the real world implications. This is a recipe for failure since the industry expects business school students to tell the story with a strong reference to the context. A simplistic understanding of the formulas is what students’ need instead of a plug and solve formula based teaching method.
This document provides an overview of computational thinking including its definition, importance in education, and four pillars. Computational thinking is defined as a process of breaking down problems into parts to solve them similarly to how computers operate. It is important for improving student confidence and enabling active participation. The four pillars are decomposition, pattern recognition, abstraction, and algorithms. Examples are given of how computational thinking could be applied in history and English classes by giving students open-ended tasks to research and draw conclusions. The document concludes with links to a video and quiz about computational thinking.
This document discusses initiatives to improve math literacy for college students by connecting MyMathLab, course redesign, and Quantway programs. It outlines problems with traditional developmental math sequences and solutions being tested, including Statway and Quantway programs. The Quantway approach focuses on numeracy, algebraic reasoning, proportional reasoning, and functions through application-based integrated lessons. It balances instruction methods and assesses students with online homework, projects, and tests emphasizing both skills and concepts. The goal is to give underprepared students mathematical maturity to succeed in college-level courses in one semester through this new quantitative literacy focused curriculum.
The document provides guidance on solving physics problems using a general 5-step strategy and the KUDOS method for word problems. It begins with an overview of the learning objectives which are to learn a general problem-solving technique, how to solve word problems, how to prepare for exams, and tips for taking exams. Examples then demonstrate applying the 5-step general strategy and the KUDOS (Known, Unknown, Definitions, Output, Substantiate) method to solve sample physics problems step-by-step. The strategies provide a systematic approach to breaking down problems and connecting known information to unknowns through definitions and equations.
Developing conceptual understanding of probabilityA CM
1) The document discusses the importance of teaching mathematics for conceptual understanding rather than just rote learning of procedures. It emphasizes building relationships between mathematical ideas.
2) Several realities in modern classrooms are discussed, such as students applying algorithms without understanding. The significance of problem solving for developing conceptual understanding is also covered.
3) Activities are presented to help teachers promote conceptual understanding, for example having students explore concepts like probability by analyzing real-world tasks and data. Discussion of how to assess conceptual learning is also included.
The document provides an overview of symbolic machine learning approaches. It discusses how machine learning allows systems to learn intelligent behavior from experience rather than being explicitly programmed. It outlines different types of symbolic learning approaches that will be covered, including inductive learning, rote learning, nearest neighbor classification, and Bayesian classification. Key algorithms like nearest neighbor and examples of their applications are also summarized.
1 Saint Leo University MAT 131 College Mathemati.docxaryan532920
1
Saint Leo University
MAT 131
College Mathematics
Course Description:
Topics include critical thinking, number theory, measurement, percentages, geometry, counting
methods, probability, and statistics.
Prerequisite:
None
Textbooks:
Blitzer, B. (2011). Thinking mathematically with Mymathlab plus access (6th ed.). Boston, MA:
Pearson-Prentice Hall. ISBN-13: 978-0-321-86732-2
White, J., & White, S. (2015). Thinking critically to solve problems: Combining values and
college mathematics. Boston, MA: Pearson-Prentice Hall. ISBN-13: 978-1-5115-3917-3
The MyMathLab Plus access code includes Thinking Mathematically (Blitzer) eBook
access, so purchasing the physical Blitzer textbook is optional.
Learning Outcomes:
By the end of this course, students will be able to:
1. Solve problems involving data analysis and probability and obtain a better sense of
community when interpreting studies that relate to the world around them.
2. Use concepts that relate to number sense, concepts, and operations.
3. Use measurement techniques and demonstrate knowledge of geometry and spatial
sense.
4. Use basic problem-solving strategies.
5. Explore how mathematics can be used to enhance community.
Core Value:
Students will be learning the mathematical skills for solving problems and then investigate how
those skills and solutions can be used to enhance community.
Community: Saint Leo University develops hospitable Christian learning communities
everywhere we serve. We foster a spirit of belonging, unity, and interdependence based on
mutual trust and respect to create socially responsible environments that challenge all of us to
listen, to learn, to change, and to serve.
2
Evaluation:
In determining the final grade, the following weights will apply:
Problem Sets (7 @ 2% each) 14%
Quizzes (4 @ 2% each) 8%
Exams (2 @ 13% each) 26%
Final Test 20%
Discussions (8 @ 1% each) 8%
Group Project 12%
Individual Project 12%
Total 100%
Module Breakdown of Percentages:
Module 1: Problem Set 1 = 2%, Discussion = 1%
Module 2: Problem Set 2 = 2%, Discussion = 1%, Quiz 1 = 2%, Exam 1= 13%,
Module 3: Problem Set 3 = 2%, Discussion = 1%
Module 4: Problem Set 4 = 2%, Discussion = 1%, Quiz 2 = 2%, Group Project = 12%
Module 5: Problem Set 5 = 2%, Discussion = 1%
Module 6: Problem Set 6 = 2%, Discussion = 1%, Quiz 3 = 2%, Exam 2 = 13%
Module 7: Problem Set 7 = 2%, Discussion = 1%
Module 8: Discussion = 1%, Quiz 4 = 2%, Final Test = 20%, Individual Project = 12%
Grading Scale:
Grade Score (%)
A 94-100
A- 90-93
B+ 87-89
B 84-86
B- 80-83
C+ 77-79
C 74-76
C- 70-73
D+ 67-69
D 60-66
F 0-59
A minimum grade of “C” is needed to fulfill the degree requirement.
MyMathLab:
Most of your assignments for this course will be completed in MyMathLab, which is designed to ...
Solving Equations by Factoring KTIP lesson planJosephine Neff
1) The document is a lesson plan for teaching 9th grade algebra students how to factor quadratic equations and use factoring to solve equations and real-world problems.
2) The lesson involves reviewing factoring patterns, teaching students to factor quadratic equations in standard form using various methods, and using factoring to solve physics problems involving height, speed, and time.
3) Formative and summative assessments are used to check students' understanding of factoring quadratic trinomials and using factoring to solve equations.
· Etac lesson plan teacher hickslewisweek of oct.19 23,20piya30
This lesson plan outlines math and science instruction for 1st grade students over the course of a week. The plan focuses on addition and subtraction strategies, with daily objectives covering counting, making 10, and explaining strategies. Each day includes establishing objectives, modeling concepts, interactive practice, and small group or individual work. Formative assessments and adjusting for English learners are also incorporated daily.
This unit plan is for an AP Differential Calculus class taught over 5 weeks. Students will learn differential calculus methods and apply them to solve real-world problems. They will learn the history of calculus and its applications. Students will visit a company to learn how it uses calculus. The essential question is "Why do I need to know calculus?". Objectives are to apply calculus to solve problems, describe solutions verbally and in writing, and learn about its historical development and use in different fields. Assessments include weekly quizzes, tests, and a portfolio with solutions, reports and reflections.
httpsvtu.ac.inpdd2021syllabusofengineeringArjun Bc
This document provides information about the course "Transform Calculus, Fourier Series and Numerical Techniques". The course aims to teach students how to use Laplace transforms to solve ordinary differential equations, Fourier series to represent periodic phenomena, and numerical techniques to solve differential equations. The course consists of 5 modules that cover topics such as Laplace transforms, Fourier series, Fourier transforms, z-transforms, partial differential equations, and calculus of variations. Assessment includes continuous internal evaluation and a semester end exam. Students will learn to solve problems in engineering applications using the techniques taught in this course.
The document outlines the agenda and objectives for year 2 of a collaborative project between a school board and university aimed at enhancing math teaching and learning through technology. The agenda includes sharing lessons on problem solving strategies, formative assessment, and planning school visits. The objectives are to further develop communities of practice around math education and digital tools, test solutions to identified problems in student learning, and strengthen the partnership. Key activities involve video-based lesson studies, reflective practice, and continuing the professional learning network.
Learning & Teaching GCSE MathematicsColleen Young
This document provides teaching resources and ideas for GCSE Mathematics. It includes information on specification changes, assessment objectives, teaching guidance from exam boards, and problem solving strategies. Sample exam questions, topic tests, and diagnostic questions are provided. Additional resources on areas like extension materials, revision activities, and developing recall are also referenced.
JiTT - Blended Learning Across the Academy - Teaching Prof. Tech - Oct 2015Jeff Loats
This document summarizes a presentation on implementing Just-in-Time Teaching (JiTT), a blended learning strategy. The presentation provides an overview of JiTT, shares data from courses that have used JiTT showing increased student preparation and performance, and offers recommendations for getting started with JiTT. Sample JiTT questions are also presented along with student responses to demonstrate how the strategy works.
Ace Maths Unit Two: Developing Understanding in Mathematics (PDF)PiLNAfrica
In this unit, the theoretical basis for teaching mathematics – constructivism – is explored. Varieties of teaching strategies based on constructivist understandings of how learning best takes place are described
This document provides an overview of a webinar for fifth grade teachers on the CCGPS unit for order of operations and whole numbers. The webinar will focus on the big ideas, standards, and resources for the unit. Teachers will learn about navigating a CCGPS unit, new aspects of the frameworks, and strategies for developing students' number sense. They will also discuss tools for teaching number operations and developing mathematical understanding.
An Intelligent Microworld as an Alternative Way to Learn Algebraic ThinkingCITE
This document summarizes a research project that designed and tested an online environment called eXpresser to help students learn algebraic thinking and mathematical generalization. The project involved:
1) Developing eXpresser as an interactive microworld for building patterns and expressing rules that govern the patterns.
2) Conducting design experiments with 11-12 year old students to test eXpresser and gather feedback.
3) Interviewing students and finding that eXpresser helped them articulate relationships between quantities in patterns and validate rules through animation.
4) Designing group tasks for students to share and compare patterns/rules, finding most could determine if rules were equivalent.
This document provides resources for teaching fractions to 3rd grade students using technology. It includes rationales for integrating technology, such as enhancing lessons and student understanding through visuals. The document then summarizes various online resources like blogs, videos, games and worksheets that can be used for fraction instruction and practice. These resources allow students to learn fractions interactively in order to build their skills in a fun and engaging way.
The document provides an overview of the Common Core State Standards including the goals, adoption by states, instructional shifts, implementation timeline, and assessments. It discusses narrowing the standards to focus more deeply on key concepts, building coherence across grade levels, and requiring equal rigor in conceptual understanding, skills, and application. Sample 5th grade math standards on fractions and diagrams are presented. The document emphasizes how the standards complement other initiatives to prepare students for college and careers.
This webinar provided an overview of the 4th grade CCGPS mathematics unit on whole numbers, place value, and rounding in computation. The big idea of the unit is to deepen understanding of place value and its usefulness in estimation and computation. Resources were shared for exploring strategies for teaching key concepts like multi-digit multiplication and comparing fractions. Feedback was requested to help improve future unit-by-unit webinars. Participants were also encouraged to join a wiki for ongoing discussion of CCGPS mathematics.
The document discusses a workshop on engineering mathematics course planning at Alpha College of Engineering. It covers important educational goals of promoting retention and transfer of learning. It discusses different types of learning - rote learning which focuses on knowledge acquisition, and meaningful learning which provides students with knowledge and cognitive processes for problem solving. The course plan details topics to be covered each semester including classifying topics into remembering, understanding and applying categories. It also discusses assessing students for retention and transfer of learning goals.
Use of Technology in Education, But at What Cost?IJITE
Use of technology in the field of education has been a blessing. Faster grading, quicker notes / media availability for students, interactive communication outside of classrooms with students and faculty, online courses etc. have added to the enhancement of our education system. But when technology is pushed in teaching without proper thought, it becomes a black box approach at the cost of intuition, commonsense, and overall understanding of the concepts. Instead of supplementing technology in the process of learning, it has been used in making the black box approach more common. When we can shift the question from “How to educate with technology?” to “How to teach people best, and how should we design learning experiences in light of existing technology?”, then learning becomes a way to quench curiosity, and passion for learning will become a never ending pursuit for students. Models and textbook theories can help build the knowledge base, but they miss the context [5,7]. Students take them at face value without thinking through the real world implications. This is a recipe for failure since the industry expects business school students to tell the story with a strong reference to the context. A simplistic understanding of the formulas is what students’ need instead of a plug and solve formula based teaching method.
This document provides an overview of computational thinking including its definition, importance in education, and four pillars. Computational thinking is defined as a process of breaking down problems into parts to solve them similarly to how computers operate. It is important for improving student confidence and enabling active participation. The four pillars are decomposition, pattern recognition, abstraction, and algorithms. Examples are given of how computational thinking could be applied in history and English classes by giving students open-ended tasks to research and draw conclusions. The document concludes with links to a video and quiz about computational thinking.
This document discusses initiatives to improve math literacy for college students by connecting MyMathLab, course redesign, and Quantway programs. It outlines problems with traditional developmental math sequences and solutions being tested, including Statway and Quantway programs. The Quantway approach focuses on numeracy, algebraic reasoning, proportional reasoning, and functions through application-based integrated lessons. It balances instruction methods and assesses students with online homework, projects, and tests emphasizing both skills and concepts. The goal is to give underprepared students mathematical maturity to succeed in college-level courses in one semester through this new quantitative literacy focused curriculum.
The document provides guidance on solving physics problems using a general 5-step strategy and the KUDOS method for word problems. It begins with an overview of the learning objectives which are to learn a general problem-solving technique, how to solve word problems, how to prepare for exams, and tips for taking exams. Examples then demonstrate applying the 5-step general strategy and the KUDOS (Known, Unknown, Definitions, Output, Substantiate) method to solve sample physics problems step-by-step. The strategies provide a systematic approach to breaking down problems and connecting known information to unknowns through definitions and equations.
Developing conceptual understanding of probabilityA CM
1) The document discusses the importance of teaching mathematics for conceptual understanding rather than just rote learning of procedures. It emphasizes building relationships between mathematical ideas.
2) Several realities in modern classrooms are discussed, such as students applying algorithms without understanding. The significance of problem solving for developing conceptual understanding is also covered.
3) Activities are presented to help teachers promote conceptual understanding, for example having students explore concepts like probability by analyzing real-world tasks and data. Discussion of how to assess conceptual learning is also included.
The document provides an overview of symbolic machine learning approaches. It discusses how machine learning allows systems to learn intelligent behavior from experience rather than being explicitly programmed. It outlines different types of symbolic learning approaches that will be covered, including inductive learning, rote learning, nearest neighbor classification, and Bayesian classification. Key algorithms like nearest neighbor and examples of their applications are also summarized.
1 Saint Leo University MAT 131 College Mathemati.docxaryan532920
1
Saint Leo University
MAT 131
College Mathematics
Course Description:
Topics include critical thinking, number theory, measurement, percentages, geometry, counting
methods, probability, and statistics.
Prerequisite:
None
Textbooks:
Blitzer, B. (2011). Thinking mathematically with Mymathlab plus access (6th ed.). Boston, MA:
Pearson-Prentice Hall. ISBN-13: 978-0-321-86732-2
White, J., & White, S. (2015). Thinking critically to solve problems: Combining values and
college mathematics. Boston, MA: Pearson-Prentice Hall. ISBN-13: 978-1-5115-3917-3
The MyMathLab Plus access code includes Thinking Mathematically (Blitzer) eBook
access, so purchasing the physical Blitzer textbook is optional.
Learning Outcomes:
By the end of this course, students will be able to:
1. Solve problems involving data analysis and probability and obtain a better sense of
community when interpreting studies that relate to the world around them.
2. Use concepts that relate to number sense, concepts, and operations.
3. Use measurement techniques and demonstrate knowledge of geometry and spatial
sense.
4. Use basic problem-solving strategies.
5. Explore how mathematics can be used to enhance community.
Core Value:
Students will be learning the mathematical skills for solving problems and then investigate how
those skills and solutions can be used to enhance community.
Community: Saint Leo University develops hospitable Christian learning communities
everywhere we serve. We foster a spirit of belonging, unity, and interdependence based on
mutual trust and respect to create socially responsible environments that challenge all of us to
listen, to learn, to change, and to serve.
2
Evaluation:
In determining the final grade, the following weights will apply:
Problem Sets (7 @ 2% each) 14%
Quizzes (4 @ 2% each) 8%
Exams (2 @ 13% each) 26%
Final Test 20%
Discussions (8 @ 1% each) 8%
Group Project 12%
Individual Project 12%
Total 100%
Module Breakdown of Percentages:
Module 1: Problem Set 1 = 2%, Discussion = 1%
Module 2: Problem Set 2 = 2%, Discussion = 1%, Quiz 1 = 2%, Exam 1= 13%,
Module 3: Problem Set 3 = 2%, Discussion = 1%
Module 4: Problem Set 4 = 2%, Discussion = 1%, Quiz 2 = 2%, Group Project = 12%
Module 5: Problem Set 5 = 2%, Discussion = 1%
Module 6: Problem Set 6 = 2%, Discussion = 1%, Quiz 3 = 2%, Exam 2 = 13%
Module 7: Problem Set 7 = 2%, Discussion = 1%
Module 8: Discussion = 1%, Quiz 4 = 2%, Final Test = 20%, Individual Project = 12%
Grading Scale:
Grade Score (%)
A 94-100
A- 90-93
B+ 87-89
B 84-86
B- 80-83
C+ 77-79
C 74-76
C- 70-73
D+ 67-69
D 60-66
F 0-59
A minimum grade of “C” is needed to fulfill the degree requirement.
MyMathLab:
Most of your assignments for this course will be completed in MyMathLab, which is designed to ...
Solving Equations by Factoring KTIP lesson planJosephine Neff
1) The document is a lesson plan for teaching 9th grade algebra students how to factor quadratic equations and use factoring to solve equations and real-world problems.
2) The lesson involves reviewing factoring patterns, teaching students to factor quadratic equations in standard form using various methods, and using factoring to solve physics problems involving height, speed, and time.
3) Formative and summative assessments are used to check students' understanding of factoring quadratic trinomials and using factoring to solve equations.
· Etac lesson plan teacher hickslewisweek of oct.19 23,20piya30
This lesson plan outlines math and science instruction for 1st grade students over the course of a week. The plan focuses on addition and subtraction strategies, with daily objectives covering counting, making 10, and explaining strategies. Each day includes establishing objectives, modeling concepts, interactive practice, and small group or individual work. Formative assessments and adjusting for English learners are also incorporated daily.
This unit plan is for an AP Differential Calculus class taught over 5 weeks. Students will learn differential calculus methods and apply them to solve real-world problems. They will learn the history of calculus and its applications. Students will visit a company to learn how it uses calculus. The essential question is "Why do I need to know calculus?". Objectives are to apply calculus to solve problems, describe solutions verbally and in writing, and learn about its historical development and use in different fields. Assessments include weekly quizzes, tests, and a portfolio with solutions, reports and reflections.
httpsvtu.ac.inpdd2021syllabusofengineeringArjun Bc
This document provides information about the course "Transform Calculus, Fourier Series and Numerical Techniques". The course aims to teach students how to use Laplace transforms to solve ordinary differential equations, Fourier series to represent periodic phenomena, and numerical techniques to solve differential equations. The course consists of 5 modules that cover topics such as Laplace transforms, Fourier series, Fourier transforms, z-transforms, partial differential equations, and calculus of variations. Assessment includes continuous internal evaluation and a semester end exam. Students will learn to solve problems in engineering applications using the techniques taught in this course.
The document outlines the agenda and objectives for year 2 of a collaborative project between a school board and university aimed at enhancing math teaching and learning through technology. The agenda includes sharing lessons on problem solving strategies, formative assessment, and planning school visits. The objectives are to further develop communities of practice around math education and digital tools, test solutions to identified problems in student learning, and strengthen the partnership. Key activities involve video-based lesson studies, reflective practice, and continuing the professional learning network.
Learning & Teaching GCSE MathematicsColleen Young
This document provides teaching resources and ideas for GCSE Mathematics. It includes information on specification changes, assessment objectives, teaching guidance from exam boards, and problem solving strategies. Sample exam questions, topic tests, and diagnostic questions are provided. Additional resources on areas like extension materials, revision activities, and developing recall are also referenced.
This lesson plan provides instruction for a 6th grade mathematics class on adding and subtracting fractions and mixed numbers. The plan outlines three 50-minute lessons to teach students how to: 1) add similar fractions in simple or mixed forms with regrouping, 2) subtract similar fractions in simple or mixed forms with and without regrouping, and 3) subtract dissimilar fractions in simple or mixed forms with and without regrouping. The lessons include objectives, content outlines, learning tasks such as group work and problem solving, teaching strategies, materials, and assessments. The overall goals are for students to master the four fundamental operations on fractions and apply them to mathematical problems and real-world situations.
The document discusses using a multi-modal think board approach to teaching mathematics. It describes the six mathematical modes of thinking - number, word, diagram, symbol, real thing, and story. Examples are provided of how to differentiate mathematics instruction for students using open-ended questions within these six modes. The goal is to engage students in thinking and working mathematically in a variety of ways.
This document contains a detailed lesson plan for teaching students about the mean of grouped data. It includes the objectives, which are to state the formula for finding the mean of grouped data, find the mean of grouped data, and solve problems involving the mean of grouped data. The lesson plan outlines the procedures the teacher will follow, which includes introducing the topic, discussing the concept and formula for finding the mean of grouped data, working through examples, and having students practice calculating the mean of grouped data sets through exercises. The lesson aims to help students understand how to calculate the mean when data is grouped into intervals with frequencies rather than having individual data points.
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The film The Godfather explores the theme of revenge. When Michael Corleone's father Vito is attacked, Michael seeks revenge by killing the ones responsible. This act of vengeance draws Michael deeper into the family crime business. Throughout the film, Michael takes revenge on anyone who wrongs or betrays his family, solidifying his role as the new head of the crime family. Cinematography in The Godfather features unique shots and scenes that helped introduce new techniques to films.
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The document discusses several Classroom Assessment Techniques (CATs):
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This lesson plan introduces 6th grade students to the Mayan base-twenty number system. It begins with a review of the base-ten number system. Students will then learn about the Mayan number system through interactive stations, worksheets, and games. They will compare and contrast the base-ten and base-twenty systems. The lesson celebrates cultural diversity by showing different mathematical approaches. Technology such as a SMART board and online polling site are used to engage students and check understanding throughout the lesson.
This document outlines the weekly schedule and lessons for a classroom. It includes:
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1. The document contains a lesson plan for a 6th grade math class covering the topic of "Playing with Numbers".
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This technology-infused lesson plan teaches 9th grade students about quadratic functions through a week-long unit. Students will learn to solve and graph quadratic equations and functions algebraically and graphically using tools like graphing calculators, online graphing calculators, and SMART Notebook software. Formative and summative assessments include group presentations and a unit test on quadratic functions. The lesson incorporates student-centered learning and supports various learning styles.
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An alternative learning experience in transition level mathematics
1. An alternative learning experience in
transition level mathematics
Screen captured lectures, collaborative activities, and more
Dann Mallet
QUT Mathematical Sciences
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4. Introduction and context
Introduction and context
The unit – MAB105 Preparatory Mathematics
The most elementary maths unit QUT offers
Among the most diverse cohorts (unit does not belong in any course)
“Like” high school mathematics, steep learning curve
Fundamental to vast number of degree programs
Recently lost favour, but being reborn!
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5. Introduction and context
Introduction and context
The unit – MAB105 Content
Properties of the number system
Basic algebra
Functions and equations, graphs
Linear functions – equations and applications
Systems of linear equations
Non-linear functions
quadratic, exponential, logarithmic, trig: properties, applications
Introduction to calculus
rates of change, derivatives, rules of differentiation, optimization,
applications
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6. Introduction and context
Introduction and context
The unit – MAB105 Learning outcomes
1
Solve straightforward equations and draw and interpret graphs of one
independent variable.
2
Understand the concepts involved with functions and functional
notation and in particular know the properties associated with
quadratic, exponential, logarithmic and trigonometric functions and
applications of same.
3
Understand the concepts involved with rates of change, derivatives,
maxima, minima and integration.
4
Engage in analytical thinking skills and communicate clearly and
concisely in mathematical language.
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7. Introduction and context
Introduction and context
The unit – MAB105 Assessment
Semester/Year
Items & weighting
2008
2009
2010
2011
2012
2013
Participation/Assignments 40%, ES Exam 60%
Assignments 20%, MS Exam 20%, ES Exam 60%
PST 40%, ES Exam 60%
PST 60%, ES Exam 40%
PST 60%, ES Exam 40%
PST 60%, ES Exam 40%
Fairly “standard” mathematics assessment style: heavy on exam and
assignment
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8. Introduction and context
Introduction and context
The unit – MAB105: Enrolments
MAB105 Enrolments 2008-2013
150
100
2/13
1/13
2/12
1/12
2/11
1/11
2/10
1/10
2/09
1/09
2/08
50
1/08
Enrolments
200
Semester
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9. Introduction and context
Introduction and context
The unit – MAB105: Results
Percentage of all students
MAB105 Grade distribution (all students) 2008-2013
30
20
10
0
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1
2
3 4
Grade
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10. Introduction and context
Introduction and context
How has MAB105 evolved?
Long transition – my involvement: since 2001
First press: handwritten OHTs, textbook, lectures.
A
Introduced booklet of LTEX ed notes (AC Farr, DG Mallet)
text aligned, inbuilt worksheets, reduced dependence on f2f
A
Introduced set of LTEX ed lecture slides (fill in the gap style) (AC
Farr)
text/notes aligned, reduced dependence on f2f
Introduced workbook-style version of booklet (AC Farr)
further reduced dependence on f2f
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11. Introduction and context
Introduction and context
The next step – motivation
“Tertiary institutions will be challenged not only to meet growing demand by expanding
the number of places offered, but also to adapt programmes and teaching methods to
match the diverse needs of a new generation of students.”1
“Today in education, we are witnessing an unbundling of previous network structures.
And a rebuilding of new network lock-in models.”2
“We are living in a constantly changing environment. This situation should force
teachers to constantly re-think their pedagogical philosophy.”3
1
2
3
OECD, 2013, Education at a glance 2013: OECD indicators. OECD Publishing. http://dx.doi.org/10.1787/eag-2013-en
G. Siemens, Associate Director, Technology Enhanced Knowledge Research Institute, Athabasca University
I. Czaplinski, 2012, Affordances of ICTs: An environmental study of a French language unit offered at university level. UQ.
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12. Introduction and context
Introduction and context
The next step – motivation
People are doing new, cool things in delivering learning experiences
QUT built collaborative learning spaces
Students don’t show up “just for lectures/tutorials”
Also, national/international agendas...
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13. Introduction and context
Introduction and context
The next step – a summary
So what has been done? How much effort was it? What happened?
Here’s what students experienced this semester:
No f2f lectures
Weekly workshops of various styles
Problem sheets
Expert exemplars
Clean and annotated slides
Lectures in video form
Effort = slightly less.
Results:
w.r.t students? wait til after exam. Seminar 2 in January
w.r.t. me? greater planning, better “product”, more reflection
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15. Collaborative learning ideas
Collaborative learning ideas
Overview
What can we do here? Well, besides mathematics...
Team building
Communication
Technology
Let’s take a look at some examples from this year...
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16. Collaborative learning ideas
Collaborative learning ideas
Team building
Activity: BOMDAS (you know
it? can you do it?)
Purpose: Team formation,
communication, community
building, intro/warm up
Possibilities: competitive,
enduring identification
Workshop 1
MAB105
Preparation and instructions
Before commencing the activity, make sure you are in groups of no more than 6 people. You may
use pen and paper, whiteboards, glass boards, COWs, calculators and your heads.
1. Give your group a name – decide carefully, you’ll be using it for the rest of semester.
2. Nominate one person in the group to be note-taker. The note-taker will keep a record of
discussions and decisions, as well as the final group response.
3. Nominate one person to be the scribbler. They will do any necessary writing and calculating
on the whiteboard.
4. Nominate another person to be the reporter. The reporter will report back to the class on the
group’s response to the task.
5. All group members should then read the task below.
6. Then the group should work together to attempt to come up with the best possible group
responses.
7. Finally, the reporters from each group will report back to the class to see which group has
come up with the best responses.
Background
Let’s say you were given the numbers 5, 6 and 7 and the operations of addition and subtraction. If
you must use each number and operation once, and only once, then the largest possible result is
7+6−5 = 8
and the smallest possible result is
5 + 6 − 7 = 4.
The task
Unexpected: definitions of
terms
Using each of the numbers 2, 3, 4, 5, 6 and 7 once, and only once, and each of the operations of
addition, subtraction, multiplication, division and exponentiation (raising to a power) once, and
only once, your group is to attempt to make
1. the largest number possible and
2. the smallest number possible.
When reporting back to the class, the reporter needs to the provide two numbers, as well as discuss
two decisions that the group made while attempting to find the numbers.
CRICOS No. 00213J
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17. Collaborative learning ideas
Collaborative learning ideas
Communication
Workshop 3
MAB105
Preparation and instructions
Activity: communication of
factorising/solving
Before commencing the activity, make sure you are in groups of no more than 6 people. You may
use pen and paper, whiteboards, glass boards, COWs, calculators and your heads.
1. If your table has a group name from the first workshop, reuse it. Otherwise, make up a new
group name and write your names along with the group name on the piece of paper you are
given.
2. Using the COW, navigate a web browser to goanimate.com, and have one of the group either
login using an existing account or sign up for a new one.
3. The group can either work together on the problems (for example, split the problems up with
everybody attempting only one), or you might wish to attempt them all yourself.
The task
Attempt each of the following problems either on a whiteboard, on paper or in your notebooks.
1. Factorise the expression 16a5
2. Solve the equation 3( x
36a3
1) = 2x + 4 for x
3. Factorise the expression 2t2 + 20t + 18
4. Factorise the expression 4x2
Purpose: Communication,
exploring unknown difficulties,
fun
4x + 1
Now, use Go!Animate. Use the “Quick Video Maker” and select a template, setting and characters.
In your group, choose one of your attempts at the above problems and use the two characters in
your Go!Animate video to explain what you did to arrive at your answer. If you weren’t able to
reach the answer, then use your characters to discuss the difficulties you had. You have a total of 10
lines of dialog (parts of a conversation) each of which can be only 180 characters long so you need
to be concise but descriptive to get the point across.
You might want to pretend your characters are a teacher and a student, or a really smart friend
explaining the answer to another friend. Or whatever you like.
You might choose the problem you are most confident about because you can explain it better, or
perhaps you choose the one you are least confident about because thinking about it in this different
way might help you understand it better and identify your difficulties.
Possibilities: showcase, reuse in
future
The point!
This workshop could have just involved solving equations and factorising expressions. But by
explaining and describing your maths in words, you slow down and think about exactly what you
are doing. You will also see how your written attempts at problems can appear to somebody – other
people don’t necessarily know what’s going on in your head, so it’s important to write your maths
clearly and explain it fully. This is especially important for exams because, in order to give you
marks, the marker needs to know what you mean when you write a response.
CRICOS No. 00213J
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1
Unexpected: typing maths:
difficult
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18. Collaborative learning ideas
Collaborative learning ideas
Communication
Students attempt questions,
then attempt to explain solns
via GoAnimate!
i.e. translate their maths into
words
Dann
Team temporary
Kier
Epic ninja battle
They see how poorly/well they
communicate their
mathematics by attempting to
translate it
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19. Collaborative learning ideas
Collaborative learning ideas
Technology
Activity: Modelling with
MoCOWs, BoM website
Workshop 7
MAB105
Preparation and instructions
Purpose: Real data, visualise,
interpret, model/apply
Use the MUCOW computer to obtain river height data, import it into a spreadsheet, then plot the
data. Next, attempt to develop a mathematical model, in the form of a trig function, to describe the
data.
• Go to the Bureau of Meteorology website, and the page where rain and river data is available:
www.bom.gov.au/qld/flood/rain_river.shtml
• Choose a river data set (e.g. Bremer R at Ipswich # ).
• Click on the link to the plot to check whether or not sufficient change occurs in the river height
over time to generate a visible sine curve. Then go back to the previous page.
• Click on the link to the data. This should bring up a rather long table of data values.
• Select the data and copy it. Then paste it into Microsoft Excel. Note that you may need to
paste into a text file first and then into excel
Possibilities: Lots
• Produce a scatter plot of the data.
The task
1. How high does the river go at its maximum (on average)? How low?
2. How long (time) does it take for the river to pass from its zero height up to the maximum
height, down through zero to the minimum depth and finally back to zero (on average)?
3. Use your answers to the above questions to generate a function of the form
h(t) = a sin(bt)
to model the height of the river. Here h(t) is the height of the river and t represents time.
4. Generate a new column in your excel spreadsheet that gives values of your model h(t) for the
times already available in your spreadsheet.
5. Plot these on the same scatterplot as the river data.
6. Does your model look similar to the data? What differences do you notice? How might you
overcome these differences to create a better model?
CRICOS No. 00213J
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21. Recording lecture videos
Recording lecture videos
Specs
Slides were created
using an Apple MacBook Air (11in) and Apple iMac (27in)
running Mac OS X 10.7-8
MacTex 2012, Beamer
Occasionally Wolfram|Alpha
Lecture videos were recorded
using a Samsung XE700T1A Slate PC
running Microsoft Windows 7 and
PDF Annotator 3 and Camtasia Studio 8
Hardware and software provided by the Mathematical Sciences School
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22. Recording lecture videos
Recording lecture videos
Recording process
Recording process
A
1. Produce slides using LTEX (beamer)
2. Open slides using PDF Annotator, adjust size, prepare tools
3. Open Camtasia Studio, prepare recording window
4. Record!
5. Annotate the slides using stylus and speak (teach!) as usual
Figure : Demo video
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23. Recording lecture videos
Recording lecture videos
Editing process
Editing process
1. After recording, open recording package in Camtasia Studio
2. Edit sound, cut video/sound, add video, subtitles, annotations,
pointers, graphics, etc
3. Quizzes can be added to the video
4. Save project and produce final product (video file or SCORM package)
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25. SCORM packages
SCORM packages
What is SCORM?
SCORM = Sharable Content Object Reference Model
A set of standards and specifications for web-based e-learning
Allows “sequencing”: constraining the learner’s path through the
materials
Gatekeeping: completion of materials/score threshold
Blackboard has SCORM compatibility!!!
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26. SCORM packages
SCORM packages
SCORM and MAB105
Take the video lectures recorded with Camtasia Studio
Embed quizzes at important points
Export as SCORM package
Import into Blackboard. For MAB105:
No restriction on number of attempts
Scoring of quizzes reported to Grade Centre
No completion/score restrictions
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27. SCORM packages
SCORM packages
Importing into Blackboard
Importing into Blackboard
After producing the SCORM package in Camtasia Studio:
1. Go to relevant Blackboard page (e.g. Learning Resources)
2. Click “Build Content”
3. Choose/click “Content Package (SCORM)”
4. Browse for file to upload
5. Choose the zip file of the SCORM package
6. Choose options
naming, detailed notes/info, track views (YES!)
number of attempts, scoring, completion etc
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29. Results – engagement
Results – engagement
Blackboard site access
Bb site total access counts by day
Bb site total access counts by week
800
Assessment due
600
Number of accesses
Number of accesses
2,000
400
200
0
Jul 15 Aug 1
Sep 1
Day
Oct 1
1,500
1,000
500
0
O 1 2 3 4 5 6 7 8 9 10 V 11 12 13 S
Week #
Usage is heavy in first 9 weeks (actually: looks like chlamydial
infection curve)
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30. Results – engagement
Results – engagement
Blackboard site access by day of week
Access peaks between upload and f2f time
Blackboard site access by day
Workshops
Upload
Hours
200
100
0
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M
T
W T
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31. Results – engagement
Results – engagement
Student Blackboard site access intensity
# of Students
1/2 class probably only accessing site to do assessment
Student Blackboard site access intensity
30
20
10
0
0-5
5-10
10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 65-70
Hours access over the semester
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32. Results – engagement
Results – engagement
Still to come
Usage of individual videos (# accesses, time spent)
A look at student results
more...
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