Mathematical Best Practices

There are numerous best practices to teaching math including:

• I Do, You Do, We Do
• Visual and Mnemonic Aides
• Projects
• Hands on Manipulatives
• Group Work
• Do Now
• Technology (Khan Academy, PowerPoint, Videos)

There are also numerous websites that discuss best practices for teaching math to ensure student learning and engagement:

http://www.pennsbury.k12.pa.us/pennsbury/Departments/Curriculum/Best%20Practices/Mathematics/Recommendations%20on%20Teaching%20Math.pdf

https://www.andrews.edu/sed/leadership_dept/webinars/presentationdocuments/the_effective_mathematics_classrroom.pdf

http://www.learnnc.org/lp/editions/math-CCSS-resources/7508

In my opinion, the best teaching practice for math classroom is student engagement because experience is the best teacher.  That is why I prefer project based learning (PBL) strategies.

Projects for Learning about Polynomials

Linking math to the real world can be challenging however through projects this can be a fun and educational experience.  Through projects we can engage our students and also deepen their understanding of topics and build skills that can helpful both inside and outside of the classroom.

Here are some interesting links I found on the internet:

http://wveis.k12.wv.us/teach21/public/project/Guide.cfm?upid=3323&tsele1=2&tsele2=108

http://wveis.k12.wv.us/teach21/public/project/Guide.cfm?upid=3488&tsele1=2&tsele2=116

http://wveis.k12.wv.us/teach21/public/project/Guide.cfm?upid=3473&tsele1=2&tsele2=116

https://prezi.com/iattne9q6dpu/polynomials-and-roller-coasters-math-project/

I specifically like the integration of the project "It's All Fun and Games" found on page 8.11 in this instructors Lesson Plan for Unit 8 on Polynomials:

http://www.montereyinstitute.org/courses/Algebra1/PD8_RESOURCE/Algebra%20I_PD_U08_InstrGuide_v1.1%20.pdf

Through this project, the students not only learn the history of mathematics and build their research skills but also improve their problem solving skills, collaboration skills, use their creativity and present their understanding of polynomials through the use of technology.  It's fun and educational!

Cultural Context of Students

In order to be an effective teacher I will have to know my students and understand their learning styles.  Having this information will help me gear my lessons and incorporate activities and resources that will help my students learn.

I will be teaching in an Arizona secondary school and although I have not yet entered the secondary classroom, I have learned that the classroom consists of Americans, Hispanics/Mexicans and with the majority of students being Native Americans.  Therefore, I must understand the learning styles of these groups if I want to be a successful teacher.  Here are some basics for Native American Learning Styles and the key factors around which I will have to tailor my lesson plans to ensure I can make a connection with my Native American students.

As a result of the various learning styles present in my classroom, I have decided that I will take a more cooperative learning approach and provide lots of visual aids such as graphic organizers, algebra tiles, and group activities for my students.  Although, these students come from homes that speak a native language other than English, I should have very few students that actually fall into the ELL category and require additional support (I learned this through previous research).  For those students who do require the additional support, I feel that having other students who speak the language come to my aid will be the most beneficial strategy because some of the languages spoken by the Native Americans in the classroom do not have a written language.  Therefore, strategies such as pairing ELL students with advanced students and reciprocal teaching will be a great practice.  

Ethics in the Classroom

I will attempt to make my classroom one that is not only structured but also nurturing.  I will have some classroom ethics, standards and expectations that will allow for fairness, creativity, quality communication and collaboration.  I want to help my students not only become smart but also become good.  And in order to do this, they will need to have character.  Therefore, I will ensure that I define character for  my students and let them know that there are two components of character: performance character and moral character.

As you know, performance refers to the outcome such as getting good grades and achieving something.  Therefore, performance character is referring to the student doing his or her best without regard to the outcome.  Whether you reach your goal or not, the fact that you tried your best means you learned along the way and are on the right path to achievement.

Moral/ethical character will also be on our top list of good character because refers to doing the right thing.  Good moral character asks for the student to respect others, be responsible, and be honest.  For a student to have character, they must have both performance character and moral character.

I will attempt to create a healthy environment and a good culture in the classroom on the first day of school.  I can promote this request for ethics by involving the students in the decision making process to establish norms and procedures for the classroom.  I will create a culture in which the students will not only do their best but will also bring out the best in each other.  Some of the key things I will be looking for when it comes to doing your best is (1) be prepared, (2) work hard, and (3) have a positive attitude.  When it comes to treating others with respect and care, I will be advising that students (1) treat others as they want to be treated, (2) use good manners (e.g., say thank you), and (3) help each other (e.g., provide constructive criticism not a put down).

Adapted from the State University of New York

Assessments

I will use a variety of assessments for my students to ensure that I accurately determine the level of learning and improvement being presented by each student.

Formative assessments will include daily Exit Tickets, Homework Tickets, and Student-to-Student Assessments.  I will also attempt for a more collaborative learning environment which should allow for increased class discussions and group activities which will be a great way for me to hear what the student thought process is while working on a problem/concept.

I will use summative assessments such as a comprehensive exam at the end of a unit along with peer-evaluations after learning specific concepts and mastering specific big ideas.  Sometimes students are simply not good test takers, and thus I will also be looking into asking my students to work on projects and create presentations for the class in an attempt to help them make connections with the real world.

I will also ensure that I allow for alternative assessments for my students such as ELL students.  I can give ELL students verbal instructions and extra space on the test to show their work.  I can also offer the students a copy of the exam in their native language but require them to respond in English.

I came across a video on Highlighting Mistakes: A Grading Strategy which I would like to incorporate into my lessons.  This grading strategy indicates that I should focus on sharing the most common mistakes with my students when going over homework and/or tests.  Instead of writing the percentage or letter grade on the test, I simply highlight the mistakes and give it back to the student. This will get the students away from thinking that grades are the most important thing, it will help them lean towards learning and more accurately continued learning. Because after giving the test back to the students, as a class, we continue the learning process by going over those mistakes and how to correct them.  This is a great strategy to continue learning and have great engagement from the students.

Arithmetic with Polynomial and Rational Expressions: Objectives, Topics and Skills

http://www.corestandards.org/Math/Content/HSA/APR/

http://www.shmoop.com/common-core-standards/ccss-hs-a-apr-1.html