Teaching Resources

15 Ways to Support Math and Science Education

joshwilkersonLeave a comment

List courtesy of the National Math and Science Initiative.

(I’ve highlighted in red the items that I especially agree with or am trying/will try to implement for my own students)

  1. Think and speak positively about math and science. Never again say to your child, “I wasn’t good in math either. Math is hard.” Rather say, “Learning math is critical for everyone today. I sure wish I had studied it more.” Encouragement and praise can be the first steps toward success.
  2. Pay attention to math and science teaching in your child’s school. Have you reviewed your child’s science or math homework lately? Are assignments or projects creative and tied to real-life situations or your child’s interests? Ask the PTO to schedule a presentation by the math and science departments at your child’s school so that you can better understand what’s being taught – and school leaders will see that parents expect quality.
  3. Support more modern lab equipment in local schools. Does the equipment in your child’s science lab look like what you used when you were in school? Times have changed and many school labs need to be updated. Do you belong to a club, or another type of organization that might help raise funds for more supplies and better equipment at your school?
  4. Stand up for algebra. Does your child’s school offer 8th grade algebra? If not, speak up to your school leaders and school board. Algebra is the gateway class that enables all students, no matter what their fields of interest, to move forward in school and college. If you don’t feel comfortable going to school leadership and/or the school board alone, you can see if other parents agree. Are there other parents like you who would support either signing a letter or going with you to a PTO meeting to try to enlist support from other parents?
  5. Become an advocate for Advanced Placement* Program courses that give students strong preparation for college work. Find out if your child’s high school offers Advanced Placement courses in math and science. If not, see if other parents would also want more information on these rigorous courses. Together you can show that parents are interested in having their children participate in AP courses. If the school already offers AP courses, find out how hard it is for students to get into the advanced classes. Advocate for a system that registers students for advanced classes unless their parents opt them out. You also should check and ensure that they are offered at non-conflicting times so students won’t miss out on helpful classes.
  6. Encourage your school leaders to provide incentives for students to successfully complete AP exams. Better yet, you can become a donor yourself – or recruit donors to defray the cost of taking exams and provide financial incentives for students to pass the exams. Do you have contacts with corporations that appreciate the need for a math-literate workforce? Do you have ties to sororities, fraternities or faith-based organizations? Look for people you know who might be willing to partner with the school to provide incentives for students who are taking rigorous AP courses. Might they also be willing to provide incentives for the teachers involved who are doing so much additional work with the students in the AP courses?
  7. Offer to mentor students in local schools who may be struggling or want to do advanced work. Recruit others to help. Is your service organization, professional group, or faith-based organization involved with your school? If not, are you willing to ask for their participation? Education ministries and service organizations can be a great source of support from retirees and others who might be willing to assist with tutoring/mentoring/grant writing.
  8. Encourage more colleges and universities to provide math and science recruitment programs for high school students. If you are a member of a civic or service organization, you could encourage the group to help organize a summer instititute for middle and high school students in math and science at a local university or college. Or, urge the university or college that you attended to reach out to high school students with special math and science programs.
  9. Volunteer to help organize a science fair if your middle school does not have one. Get the parents who are in science, health, engineering and computer fields to serve one afternoon as judges. Get local businesses to offer prizes.
  10. Rally local business support for math and science careers. Encourage your employer or chamber of commerce to form a partnership with a local school to support students who are interested in careers in math, science, computer science, and engineering. Summer internships and scholarships can make young dreams come true.
  11. Encourage more college students in math and science to become teachers. Find out what your local colleges and universities are doing to graduate more qualified math and science teachers. Are there programs in place to encourage more math and science majors to become teachers? Would a teacher training program such as UTeach be feasible there?
  12. Encourage foundations in your area to provide greater support for math and science education. Is there an organization in your community that might be interested in helping with funds for new textbooks, school supplies, lab equipment, scholarships for math and science? You should give them a nudge.
  13. Support more opportunities for girls and women in math and science. Find out if your school district offers the option of single-sex public schools. If not, encourage your school to look at the success of schools like Austin, Texas. Experience has shown that female students perform better at math and science in single-gender schools. Or, you can help more women pursue math and science careers in college by encouraging the creation of more scholarships for female students to enter those fields. Do you know any women’s service groups and foundations that might be helpful? Although more than half the students in medical schools today are women, the percentages of women in schools of engineering and most other sciences is still low.  You can help by providing a grant through a local foundation, non-profit or university that will help pay for childcare help for female graduate students and post-docs.
  14. Support more opportunities for underrepresented groups in math and science. Hispanic and African-American students are still under-represented in AP courses and in math and science classes in college. In 2000, only 4.4 percent of the science and engineering jobs in the United States were held by African Americans and only 3.4 percent by Hispanics. More minority participation is needed to provide the infusion of talent that our country will need in these critically important fields. You can help by supporting grants, scholarships, summer programs, and internships that bring more diverse students into math and science study.
  15. Urge your representatives in Congress to fund the America COMPETES legislation. The legislation was overwhelmingly passed by Congress in 2007, but has not yet been funded. The legislation cannot make a difference without funding.

Math and Music

joshwilkerson4 Comments

Mathematics and music have a long and storied history together. Extensive writing has been done on the relationship between these disciplines (see above for example). To this extensive writing I have contributed absolutely nothing, so the point of this post is not to offer any ground-breaking new ideas on the matter. The point of this post is to accomplish three things:

  1. To introduce, albeit briefly, the unique bond between these subjects for those who might not have been aware and provide links for further inquiry. Check.
  2. To offer some ideas (and hopefully get some back) for those interested in taking advantage of their students’ musical interests in order to engage them in mathematical thinking.
  3. To promote what I feel is some top-notch, musically creative, theologically deep and meaningful, Christian music that is currently being produced.

A Math Music Lesson Plan

If there are two things I can say with certainty about my students in general it is this: they don’t like math, but they do like music. They will quickly become bored with a worksheet and, as their mind drifts to other things, they will almost subconsciously start laying down beats of popular songs on their desks. So I ask myself this question: how do I tell my students that what they are doing has equal (and in reality probably greater) mathematical value than their worksheet without receiving a look back from them that implies I need serious mental help?

I offer up this lesson plan as a possible first step. I’m afraid I don’t know enough music to make this lesson as dynamic as it could potentially be. Hopefully in my free time (I’ve heard such a thing exists and I’m looking forward to experiencing it someday) I’ll be able to glean some insights from that extensive writing and make some improvements and additional lessons to exploit a connection that desperately needs exploiting. If there is anyone out there with their own suggestions, they would be greatly appreciated.

In case you are interested here is the typed lesson plan with student handouts.

Sample Lesson: Amplitude, Period, and Applications of Sinusoidal Functions (Pre-Cal)

Objectives/TEKS: The students will…

  1. …define the amplitude, period and frequency of a sinusoidal function.
  2. …discover how modifying the amplitude/period affects the graph of sine and cosine.
  3. …correlate their understanding of general transformations from Algebra II to the specific transformations of amplitude and period.
  4. …apply transformations of sinusoidal functions to sound waves and musical notes.
  5. …learn to value the influence mathematics has on discussions of beauty in music.

Scripture:

It is good to give thanks to the Lord, And to sing praises to Your name, O Most High; To declare Your lovingkindness in the morning, And Your faithfulness by night, With the ten-stringed lute and with the harp, With RESOUNDING MUSIC upon the lyre. For You, O LORD, have made me glad by what You have done, I will sing for joy at the works of Your hands.

Psalm 92:1–4

Materials:

  1. Unit Circle that the students have been assembling throughout the semester
  2. “Audacity” audio software, laptop, and projection device
  3. Handouts: student notes and worksheet

Opening:

The students will be introduced to the “Audacity” audio software. This software displays a graphical representation of sound waves for any given piece of music. This software can also play a single note and display the corresponding sound wave, which results in a perfect sinusoid. The students will note that sound waves are modeled by a sinusoidal function. (In the previous lesson the students used their unit circles to derive the graphs of the sine and cosine functions).

Various notes will be played with the similarities and differences in their graphs being discussed. The question will be posed: how can we modify the way we write sinusoidal functions to model these changes that we observe in the sound waves of various notes?

Introduction of New Material:

The students will be presented with the terminology of amplitude and period as descriptions of sinusoid graphs. The students will then discover how amplitude and period are affected when constant coefficients A and B are introduced into the expression for the sinusoidal function: y = A sin (Bθ). The students will do this using pages one and two of the attached notes, completing a table of values and then sketching the graphs.

Guided Practice:

The students will then use their understanding of amplitude and period to graph several sinusoids without a chart of points – considering the graph purely as a transformation of the sinusoidal parent functions. This can be seen on the third page of the attached student notes.

Independent Practice:

The students will be given several problems on a worksheet similar to those presented in the guided practice section.

Closing/Assessment:

Returning to the “Audacity” audio software, the students will be asked to apply their knowledge of amplitude and period to their previous descriptions of how the sound waves varied between different notes.

For example, at the beginning of the lesson when the students were asked to describe the change in the sound wave that resulted from a move from an A to a G, answers will fall along the lines of: “The graph has more repetitions” or “the graph repeats itself sooner and more often” or perhaps even “the graph repeats itself more frequently.”

Now at the close of the lesson, the students’ answers should fall along the lines of: “The period is decreased/increased” and “the frequency is increased/decreased.”

Sample questions can include:

  1. If we modify the frequency (inverse of the period) of the sinusoid, how does that change affect the musical note that is produced?
  2. Based on the answer to (1), if we want to produce a higher note, how should we modify the period? If we want to produce a lower note, how should we modify the period?

Extension Questions:

  1. What can we glean from the fact that a perfectly played musical note produces a smooth and symmetrical sinusoid, while an off-key note does not?
  2. Can we classify certain music as good and certain music as not good? In other words, is there such a thing as objectively good music? How does math contribute to this discussion?

Josh Garrels

If you have never heard of Josh Garrels, do yourself a favor and check out his music. In a world of contemporary “Christian” music that produces a lot of fluff (for lack of a better word), Josh’s music stands out as being both theologically literate and musically creative. I’m sure you’ll catch me using phrases from his songs in various postings.

Other Lectures on Math and Music

The Geometry of Music

Why Are Pianos Out of Tune?

…knowing that as (teachers) we will incur a stricter judgment

joshwilkerson2 Comments

This completes the title from my previous blog posting coming from James 3:1.

It was interesting that not long after I published that post on the genuine frustrations and questions I have from this first semester of returning to teaching, I attended a professional development on assessment. For those not fluent in teacher-speak, assessment is the term that is applied to whatever action the teacher takes to make sure the students learned what they were supposed to learn. This is most generally thought of as a test or exam.

While tests and exams are certainly types of assessments, to think of them as the only means of assessing student progress is to be a poor teacher. Assessments can take many forms and the best assessments are inseparable (and usually indistinguishable) from the content and activity of the lesson. In this way they arise naturally from the intellectual pursuit the students are undertaking (i.e. students don’t feel like they have just explored the Pythagorean Theorem through a group construction exercise but then have to take a silent, individual, paper quiz on the topic) and have high student involvement and ownership (i.e. students assess themselves and their peers progress through each step of the learning process – the activity is designed in such a way that students ask themselves “Do I know this action is correct? Is this the right way to proceed? Why?”).

This is not to say that I am an expert at developing such assessments or that I think tests should be done away with (I still give them). I simply want to point out that assessment can take many forms and that most often that form is in guiding and correcting questions during cognitive exploration rather than in a make-or-break final examination.

Which brings me back to the passage from James. Though this passage looks toward the future and the judgment (or assessment) we will have before the throne of God as people of authority and influence in the shaping of understanding and practice, I don’t think that is the only assessment we can expect to encounter. God gives more than just a final exam because God is not a poor teacher.

We are constantly being assessed and corrected by the grace of God. And as with the best of assessments we usually don’t even know that it is there – it is just a natural process of working to improve our lives bother personally and professionally. We should constantly be asking ourselves as God’s students “Do I know this action is correct? Is this the right way to proceed? Why?” Only our answers aren’t being drawn from a foundational knowledge of mathematical principles, but rather a foundational knowledge of God, His character, and His redemptive actions.

In the larger context of the 3rd chapter of James, James is discussing the dangers of the tongue and the need for believers to be very conscious of the power of words. Sometimes teaching is more about what we don’t say than what we do say. Sometimes we have to hold our tongue not just toward students but to fellow faculty, administrators, and parents. Even though we desire badly to justify ourselves before others, in reality we don’t have the authority to make that assessment. Only the Teacher holds that authority.

I’ve been reminded this semester that it is only God I should be working to please. The above was my attempt to explain that. I don’t think I have fine-tuned the assessment metaphor yet, but I wanted to go ahead and share my thoughts anyway…even though they aren’t perfect.