In my few years of teaching mathematics and assisting with courses and recitations at a university, I have quickly found that more and more learning is moving online. With so many great resources at our disposal we can assist students in their journeys to understand the material much better when we know how to utilize these resources. But where do we find them? I have spent hours prowling around on the web trying to find the best precalculus and calculus resources. I hope to write a post soon on the free online calculus resources! Below I list the best ones that I have found. These are lectures, applets, videos, and more that help to break down complex mathematical ideas into easy to understand bits of information, no matter what your student’s learning styles are.
Why do we, as educators, need more online precalculus resources?
While a lot of learning has been moving online, it is especially important to focus on this during the current crisis with COVID-19. Many schools are closed and teachers are now left trying to restructure their classrooms to provide the best education they can while also learning a new skill, which is online teaching. However luckily, the list below will help ease this journey as there are many free teaching resources online than can help with STEM classes, such as precalculus, calculus and statistics. These free online resources aim to help math teachers with a traditionally in-person subject navigate the world of online teaching to help students learn, and assess their understanding in real time.
How can students benefit?
During this current crisis, which has led to much uncertainty with our health, safety and education, many students can be confused and disappointed with this turn of events. However, there may be a silver lining for those of us who can remain hopeful and optimistic. At this time, never before have there been so many free online resources for teachers and students to aid in the study of mathematics and precalculus in particular. We can hopefully view this time as an opportunity to see what else is out there and add to our teaching toolkits.
One advantage of online learning and teaching resources for mathematics, is that a variety of free tools can be used in tandem to help target students with different learning styles, and students who learn at different paces. With the use of applets, lectures, videos, and more, students now more than ever can take advantage of a variety of content to get a full understanding of the material.
What are online precalculus resources?
There is a variety of free online resources for mathematics learning available. Below, this list includes everything from open textbooks, applets, graphing tools and homework assignment software that helps students show every step of their work, instead of just the solution. Help all your students to understand the material with videos, lessons, and more. There are many creative solutions to help teach students the material and save you an incredible amount of time.
How do we best use these resources?
Some of these resources are meant to be complimentary, used for lessons, used for practice or to help with assignments. You are the expert of your own classroom and know what your goals are for your students. While there are some resources that are quite comprehensive, it is suggested to use these resources to compliment your teaching style and fit with the requirements at your school. Please comment below with how you are using online tools in your classroom. Every school, class, and teaching style is all different and so it is advisable that we check out these tools and decide which ones work best for us. Please let me know what you think and which ones you have already tried, or are excited to try!
Below are ten of the best online precalculus resources that I have found around the web:
This free worksheet generator is a great timesaver for teaching precalculus. There are so many concepts in precalculus that involve graphing and this free online tool makes creating graphing worksheets so easy. This is also helpful because many textbooks provide only a limited amount of practice problems and other graphing style resources. Now, with a worksheet generator, you can make more problems to help your students understand the concepts fully before moving on to the next sections. These customized worksheets are able to be created in just a few minutes, saving you valuable time.
Desmos is a great, free interactive graphing tool. It also includes a collaboration feature to help students stay connected and ask questions to each other. Especially now with online learning, we can all miss the feel of our classrooms and miss the student interaction. This great feature helps students not only learn and practice their graphing skills, but can also allow students to get that collaborative spirit back. Desmos also has ready made classroom activities to help break up the monotony of reading textbooks and allow students to learn the material in new ways.
This incredible learning library has many resources for precalculus topics (in their Integrated Math I, II and III sections), and includes downloadable student lessons. Now students can work at their own pace and also practice with ready made downloadable skills practice problems. Each lesson has a comprehensive overview and includes what materials are needed, what learning goals there are, and what lesson standards are covered. There are even videos for each lesson overview, to help the students learn visually as well. For a free resource, this is a very comprehensive lesson planning tool for precalculus and other high school math classes that can easily integrate with any online classroom!
CK-12 is an incredible free online resource that includes CK-12 made content such as Precalculus texts and videos, as well as a wealth of community added resources. This website has free tools for a variety of subjects, so feel free to use for any other classes you or your colleagues may teach! One main advantage of using CK-12 is that they offer fully customizable Flexbook Textbooks, which are also digital and can be viewed on tablets, chromebooks, laptops and more. We all know how important customization is in our classroom since we all have different needs. This free tool makes that easy to do digitally.
What is special about the Free Math App, is that it allows online grading to be done much more effectively. Many online homework and assignment tools only grade automatically based on whether or not the student gets the final answer correct. However, as math teachers we all know that how a student gets to their solution can be much more important than the final solution itself! This free tool has students type in their work in order to solve a problem and allows grading based on the work. It also analyzes which problems students struggled with the most. Hopefully this tool can help save many teachers time and headaches with grading and assigning homework online!
This free online learning tool includes teaching resources as well as self-study help for students learning precalculus. MyOpenMath includes an online, interactive lessons, graded assessments and even some video lessons. The way that the assessments work includes a feature that provides unlimited problems with instant feedback, which can be especially helpful for students who are struggling with a particular concept or type of problem.
7. Precalculus (free, open source textbook)
Written by Jay Abramson, Valeree Falduto and Rachael Gross, this textbook aims to meet the needs of a broad audience because of the understanding that educational needs vary between institutions. Available at the Open Textbook Library, along with many other great resources, this textbook has 5 star reviews and can be a great tool for anyone hoping to gain more understanding in teaching and learning precalculus. With many classrooms moving online, students may not have access to physical textbooks anymore, and teachers looking for a great free textbook that can meet their needs and be easily available to students should absolutely check this out.
Another free textbook from Open Textbook Library, this one also boasts 5 star reviews and is written by David Lippman and Melonie Rasmussen. This textbook in particular focuses on providing real world examples of why the concepts are so important to students. Functions, trigonometry and more are covered in this book which has an emphasis on applications and understanding.
9. MIT Mathlets
This is an incredible resource from MIT mathlets. There are many interactive applets that can help bring to life many of the concepts that can be hard for students to grasp, such as sinusoids and trigonometric identity. Bringing in tools like this can really break the monotony of reading lessons and doing practice problems for students and help them see visually what is happening in an interactive way.
10. Khan Academy
No list of free online educational resources would be complete without Khan Academy. This incredible website has many videos, quizzes and classroom resources that can be easily integrated into an online classroom and help students to get a comprehensive understanding of the material.
These are the ten best free online precalculus resources for teachers that I have found. I also have some more free resources listed here and I highly encourage you to create an account on this site so that you can share all the resources you know of as well.
Please let me know what you think and join the discussion!
Leave comments below or share your own free resources in the forum.
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