Martha

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Mathematics
Statistics

Subjects: High School Algebra, Trigonometry and Statistics. Other subjects available Ph.D. in Chemistry - 15 yrs in research and academia; 22 yrs as a Sen. SW Eng. in the Satellite domain Tutored unde

Mathematics
Statistics

Lesson location

- At Martha's house: Denver

About Martha

Like my brother and father, as well as generations of others in our family, I was diagnosed with dyslexia at eight years old when I was unable to read. I was fortunate to live in a time and place that this was recognized, and a tutor, a woman in her 70s, was recommended by my school.

When I met my tutor, I was overwhelmed by both the foreignness of reading and the apparent importance of it. After working with her for six months, I was able to read and comprehend at grade level. To coax me into participating in an exercise, my tutor would include things I was interested in, like animals and adventure, or something I was good at, like drawing and math.

She taught me how to work with my mind in a positive and encouraging way and I similarly seek to identify what motivates a student, and craft a topic’s relevance to what interests him or her. I endeavor to place stepping stones between them and their aspirations so they are immediately on their way and lay the topic at hand as a beacon of progress on the path.

In selecting chemistry for my undergraduate major and for my Ph.D. discipline at the University of Wisconsin, Madison (UW), I was drawn by its beauty, simplicity and fundamental principles that I first found in geometry and trigonometry. My goal in selecting biophysics as my specialty, and therefore physical chemistry as my major department, was I hoped to reveal some underlying simplicity in the beauty of natural forms.

I passed the entrance exams in organic, inorganic, analytical and physical chemistry and so only had course requirements for physical chemistry. My physical chemistry graduate courses were in quantum mechanics, statistical mechanics, thermodynamics, kinetics and spectroscopy. These courses were off target for my apparent professional objectives but proved very useful, as was geophysics which I took as an undergraduate.

More on target were my graduate courses in organic chemistry, biology, biochemistry, and molecular and cellular biology. My thesis work included Metropolis Grand Canonical Monte Carlo simulations written in Fortran to investigate the thermodynamic consequences of electrostatic interactions between proteins and DNA as a function of DNA length, the simplest geometric variable. I graduated in 1991 at 31 years of age.

Our professional choices are driven by many factors. Initially my course of intense study was a product of family influence, personal interest and the women’s movement that came to prominence in the early 70s. The notion of a career path to follow with an understanding of expected income, status etc. was not yet well defined for women, which meant I’d be winging it. I was aware that there were many unanswered questions about how the world would function under this new paradigm.

I came to Denver after getting my Ph.D. for a postdoc at the University of Colorado Health Sciences Center (UCHSC) to investigate the electrostatic consequences of branched RNA structures that had been isolated and identified as catalytically self-cleaving in the presence of positive ions. I was interested to see if topology of a constant length, charged RNA ‘chain’ could alter its electrostatic properties and therefore its reactivity. I then worked for several years as an associate scientist in the same lab. I had seven first author publications and an equal number of middle author papers but opted not to seek a second postdoc, which is expected on a tenure track for a major university, so I could remain in Denver.

Still oriented academically, I started a tutoring service covering all undergraduate mathematics and science courses and advertised at local colleges and universities. For the two years I was accepting students, my main requests were for college algebra, general, inorganic, the two semesters of physical and the three semesters of organic chemistry.

I applied to the adjunct faculties of several Denver area colleges and universities. I taught Introduction to Statistics at Metropolitan State University of Denver (Metro), and then got a full-time position on the adjunct faculty at the University of Denver (DU) teaching thermodynamics to science majors and the three semesters ‘Science and Social Issues’ core course offered to non-majors.

Recognizing software development as my primary marketable skill, I was granted permission to sit in on courses in object-oriented programming, C++ and the Data Structures and Algorithms. In my last summer at DU, I took a position with the anthropology department to write a Visual C++ (VC++) interface for ground penetrating radar SW developed by NIST in DOS and gifted to the department for distribution to the international anthropology community. This project was successfully completed and received well by the target audience.

I was reminded that an adjunct position is likely to always feel temporary when my collaboration partner, the chairman of the chemistry department, accepted another position in California. I put my resume on monster.com emphasizing both my science and programming skills. I was interested to see what lay beyond the ivory tower and what contributions I could make there. I was 39 and about to enter the real world.

It was the dot com era and websites were being slapped together. I both didn’t have the skills they needed, and they weren’t interested in those I had. I still had confidence that an opportunity would come. I was cold called by Lockheed Martin (LM) which I had previously barely known about, to work on satellite systems and I accepted. I was made a senior software (SW) engineer, or SW engineering III, in the satellite domain.
This was a challenging transition as my peers had SW degrees and at least of seven years working in this capacity. I also didn’t have much knowledge of satellites. In general, the latter knowledge is gained during the seven to nine years in engineering I and II roles which I had skipped. This significant transition required that I set a personalized course of study to leverage my existing knowledge in a new direction.

I focused my career on algorithm development that required mathematical understanding and modeling rather than extensive satellite domain knowledge, which I was slowly gaining. In the specific case of analyzing electronic signals, the mathematical approaches are identical to that used in the Schrodinger wave equation in quantum mechanics. Almost half of my time at LM was spent working for the technology lab and collaborating with operators and the engineers developing new sensors.

This kind of work was not always available, so I also functioned in the standard roles, working to both maintain existing systems and on new development. In 2011 I sought employment at what is now Raytheon Technologies (RT). In 2015, I was asked to act in the role of test engineer III to help a program in development get past a major milestone. About a third my time at RT was spent in this capacity. Test engineering has many overlaps with the work I’d done in academia including technical writing and anomaly resolution.

About a year ago, it was time to leave RT and I entered semi-retirement. I have delved into the subjects that I could only pursue secondarily during a demanding professional career. My interest in biophysics has moved over the decades to regenerative health and I am currently studying to become a naturopathic practitioner and a Pilates instructor. My interest in tutoring fits in with the desire to help individuals access the full power of their minds not only to help us face the challenges of tomorrow but to encourage them to live more realized and full lives.

About the lesson

There is nothing as enabling in life as motivation, which in a younger person starts with curiosity and interest. The most foundational of the courses I offer including algebra, trigonometry and general chemistry can be presented as relevant to those with aspirations ranging from artists to engineers; learning a foundational topic should feel both expansive and orienting. Students gain a new enthusiasm for a topic when they have mastered an idea and it becomes second nature. They also appreciate success on homework and tests.

I have both tutored and taught in the classroom. My insight into helping others absorb and retain knowledge, came from how I have guided and encouraged myself to learn, including empathy with my mind’s struggles and not infrequent confusion. I also had good examples and instructors. What carries one through the challenging times is will or motivation and small and large successes.

Components of success are good study habits, showing all work for numerical problems in a clear fashion and keeping up with course material. Consistent effort is key. This will constitute an on-going dialog with the student, encouraging all progress made in this direction.

Between my postdoc at the University of Colorado Health Sciences center and my position at University of Denver (DU), I started a tutoring service offering all undergraduate science and mathematics courses. Usually in groups of two or three to keep the individual costs down, but also one on one, my main requests were for general, inorganic, the two semesters of physical, and the three semesters of organic chemistry.

Most of the science courses assumed knowledge of calculus and statistics concepts that some students had forgotten, and I would provide the necessary background. In addition to improving their grades on tests and homework, I was able to fix key subsets of knowledge in my students’ understanding. Central to making insights stick are repetitive reinforcement and providing several ways to arrive at the same conclusion. A fact is confirmed if one can triangulate it from two fixed points one understands intuitively.

Like tutoring, the classroom offers many opportunities to teach one on one and in small groups. On the adjunct faculty at the Metropolitan State University of Denver (Metro), I taught Introduction to Statistics. Then for two years, I worked full time on the adjunct faculty at the University of Denver (DU) where I taught Thermodynamics for science, mainly chemistry, majors and the three-semester introductory core course intended for non-majors called Science and Social Issues.

The core non-majors’ course had 60 students from all over campus: art, theater, history and political science to name a few. Some of the students had little recent familiarity with numerical problem solving and data representations which were required not only for the course work but also for the labs. In the first week I observed in each of my four labs, that many of the students were lost and seeking guidance from each other. While as a rule, they didn’t think they needed to have a ‘math mind’, when confronted with their lack, they were overwhelmed.

The second lab was a little shorter allowing me 40 minutes at the start to cover the mathematics they were expected to be familiar with already. Going forward I was sure that if mathematical concepts or methods were touched on in the week’s course material, I would address them in the context of their growing understanding. The results were impressive. More comfort with what they were doing allowed their natural creativity and curiosity to flow. One of these students changed his major to physics as a result.

A challenge when teaching statistics, in common with other technical subjects, is formulas and tables are introduced as if they are manna from heaven without the context for how they were developed. It is disorienting when a topic must put its useful conclusions ahead of the more advanced knowledge needed to derive them. I endeavor to leverage my student’s intuition that, for example, small data sets are inherently less meaningful than large ones and that tests like chi-square are methods for extracting high level conclusions when the data sets are small. I tell them where the tables come from, how they can apply in all cases, as well as when they become impracticable and what replaces them.

Another contributor to success is engaging an expert. I have worked in both academia and industry in fields requiring extensive mathematics and scientific capability. In the late 80s, I was one of the earliest large scale simulation specialists as a part of attaining my Ph.D. in chemistry. I was able to use this and later experience to transition my career from research and teaching to software engineering. While I do not recommend radical changes in career direction if there is a more gradual option available, the mindset of leveraging opportunities and experience is something I will pass onto my students.

In 1999 I secured a position at Lockheed Martin (LM) to work as a Senior SW engineer on satellite systems. LM had just crashed the Mars lander and unlike employers in the dotcom industry, they were concerned about the rigor of current SW grads and wanted scientists. Each new assignment allowed me to expand my SW, scripting and satellite domain knowledge in mainly manageable bites. The second half of my SW career was as a Sen. SW and Test Engineer at Raytheon Technologies (RT).

There are always opportunities to teach. Once I left academia, I helped adults, one a personal friend, and the other the wife of a coworker reach their professional goals by offering weekly tutoring sessions in General Chemistry and College Algebra respectively. I was also asked to tutor the children of friends’ ranging in age from seven to 15 and was exposed to Common Core Math Standards (CCMS).

When examined the CCMS are primarily bookkeeping methods to organize work that are identical to the more traditional approaches. When the traditional and core methods are worked in parallel, insights are gained into both. This is an excellent example of triangulating a concept; two approaches leading to the same conclusion solidifies understanding. At worst, the CCMS provide some overhead towards the worthy goal of showing all of one’s work.

I left RT about a year ago and am now in semi-retirement. I have many goals during this exciting phase of my life. To help children and young adults move past learning barriers, gain confidence through achievement and develop their interests into life pursuits is high on the list of meaningful tasks.

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Subjects: High School Algebra, Trigonometry and Statistics. Other subjects available Ph.D. in Chemistry - 15 yrs in research and academia; 22 yrs as a Sen. SW Eng. in the Satellite domain Tutored unde

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Subjects: High School Algebra, Trigonometry and Statistics. Other subjects available Ph.D. in Chemistry - 15 yrs in research and academia; 22 yrs as a Sen. SW Eng. in the Satellite domain Tutored unde

Lesson location

About Martha

About the lesson

Rates

Rate

Pack rates

Other tutors in Mathematics

Miriam

Sarah

Alyssa

Liesa

Brynn

Justice

Divya

Iryna

Patience

David

Lizzy

Sean

Sean

Kayla

Schyler

Melinda

Shira

VED

Raanan

Jaiza

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