Math report CCHS

Brian Kane 

May 2004.

Mr. Raue CEO, Mr. Ashley (Principal), Mr. Mohnen, Mr. Cadwell.

I have been extremely grateful for my experience at CCHS.  In particular I have appreciated the help given by Mr. Scott Raue CEO and the Principal Mr. Joe Ashley in completing the paper work and subsequently employing me.  I’ve really enjoyed working with my colleagues especially those I shared daily experiences with on the third floor.  My decision to leave and go back to Australia has been prompted by a downturn there in job opportunities.  My school granted me leave for 18 months and we had intended to stay at least two years at CCHS.  Our decision to return has been purely economic with regard to my age of 55 and my future prospects of employment – we have loved working with the staff and the students.

I wish to offer some observations in an entirely helpful way.  They are meant to be constructive and in no way meant to be criticisms.  I realize that I have come from Australia and this is a different style of education here but I have 30 years experience in teaching Math mainly with Indigenous people so I feel I have the background to offer some suggestions to help improve learning for the students here at CCHS.

My teaching load for 2003/2004 at CCHS:

·        4 classes of Algebra 1

·        2 classes of Geometry

Maths requirements 9- 12

·        The handbook states that 3 credits are needed and Algebra 1 is required by the State of South Dakota.  All courses have a rating of I credit.

External Pressures

·        NCLB : helping the scores to improve.  This involves teaching during the school year with the SAT testing in mind.  In 2002/2003 apparently the scores went up 17% - while it was an excellent result perhaps the topic could be discussed - how did this happen?  Was it excellent teaching, were the students more academically better, was it because the previous years results were low?

·        Preparation for College: so that the students don’t find too much of a gap between High School and College.

Testing

To test the students current ‘basic’ background, understanding and knowledge I have attached the test which was given on March 17^th  in preparation for the SAT test to all the students I teach.  The summary of the results can be found below:

Topics tested included basic decimals, percentages, fractions, algebra, area, circumference, volume and indices.

Scores according to year level

Test conclusions:

·        The majority of students really struggle with basic math concepts.  This is born out by Mr. Thompson and Mr. Cadwell in the workshop also when students are required to do practical math.  Most students would benefit by doing basic math to supplement Algebra 1 and Geometry.  This would also help in preparation for SAT testing.  Students seem to struggle across all grades in math.

·        The highest result was James Young 20 out of 25 correct

·        If the students struggled so much on this basic math test you can guess how they struggle to understand the concepts in Algebra 1.

My conclusions from teaching Algebra 1

·        Most students really find basic concepts difficult – please see attached one of the lessons from the Algebra 1 Saxon book and ask yourself how many of the CCHS students would understand this work, even with really excellent teaching and tutoring.  It is a great book but many students find it well above what they can handle.

·        In my opinion, Accelerated math is of limited value in supplementing Saxon Maths.  The course starts off well but after 50 lessons or so becomes very technical and unhelpful especially to most students who struggle with the concepts.

·        The Algebra 1 Saxon book is really very good but most students at CCHS could only manage the easier problems for themselves in each lesson.

 My conclusions from teaching Geometry

·        I tried ‘accelerated geometry’ for a few weeks but found it unhelpful and the concepts far too difficult for students to progress by themselves without the required background.

·        The geometry text books need updating.  The text I used was dated 1984.

Moderation of Grades

·        What does it mean when you assign a grade of ‘C’ for a student.  Hopefully it is a measure of the standard commensurate with all other high schools across South Dakota according to an agreed assessment criteria or is it merely a subjective assessment according to what individual teachers rate as a ‘C’?

·        I suggest a moderation process be established across class levels at CCHS.  If two teachers are covering the same course a grade of ‘C’ should be assessed the same way according to common criteria.

·        There seems to be a lot of pressure on teachers to give students “good grades” despite lack of attendance and achievement of South Dakota math standards.

Overall conclusions

·        I have learnt over the years to assess the knowledge of the students when they begin a concept and then build on this knowledge.

·        I found the majority of students taking Algebra 1 did not have the background to succeed.

·        I would recommend a review of how students are placed in classes according to their background.  This also applies to students who really struggle being placed in Algebra 1 classes in the second semester after missing the first 60 lessons of the school year e.g. Adam Tobacco, Bennett Comes Flying, Skylette Lee who came from special ed classes.

Letter of help: 

When I gave this test one the students wrote the following on her paper which summarizes what I am saying:

“I know how to do math, but not so good, I can work good as a class.  But when I am on my own I have a hard time.  I know I’m smart and everything, it’s just that it seems like I have a lot of trouble with math.  Math is not one of my good subjects – I wish it was.  If you would please sometime help me, you know, like maybe one day when you’re not doing anything.  Tutoring in math would be great.  I would really appreciate it.  Thanks”

Recommendations:

·        I have visited most of the web sites of the High schools in South Dakota and almost all just teach the standard Algebra 1, Geometry courses.  Only one to two seems to offer consumer math or general math.  General math was offered here at CCHS some years ago.  I would recommend introducing general math again before students take on algebra 1.  It is in the handbook at the moment with a credit of 1.0 but was not offered 2003/2004.

·        An assessment should be made of what the students actually know at the start of the school year in the form of a math matrix grid.  As students achieve mastery of the South Dakota Math standards, they can be marked on the grid.  There would be a separate grid for each student and the accomplishment of the standards is color coded to show some students achieving mastery in a faster time frame.  This grid can be done in middle school and would be very helpful in placing students in math classes in the High school. 

·        The Geometry text books should be modernized.

·        Mr Cadwell suggested that we shouldn’t be seen to be going backwarks taking the students where they are at because the gap between the High School and College would widen.  To overcome this problem, I suggest that many students could benefit from a bridging course.  But maybe this is impractical in the US.

·        Most of the students want success and seem very contented if they are copying but surely we can offer something else better by giving them work appropriate to their learning level.  This will enhance achievement and self esteem.

·        During 2003/2004  six classes were taught of pre-algebra in the High school.  I suggest a forward plan of 3 years at CCHS to improve maths standards by

§        shifting the pre-algebra courses to the middle school.

§        reducing pre-algebra courses in the High school to one or two.

§        Students who are academically ready do Algebra 1 as freshman and those who are not ready either do pre-algebra or General Math as freshman

§        In the second year pre-algebra students move to General Math courses, Algebra 1 students to Geometry

§        In the third year, General Math students move to Algebra 1 and Geometry students to advanced math.

§        In short I suggest a pathway grid showing courses offered and where students progress to:

Math for Native American Students: suggested ideas to be incorporated into General Math at CCHS 2004/2005

·        Similar to Aboriginal students in Australia, Native American students are more visual learners.

Traditional approach of math teaching

·        Math has no relationship to culture

·        There is no connection between real life and math.  Math exists in the classroom and in textbooks.

Multicultural approach

·        Teachers instruct using activities and games

·        Students work independently in groups

·        Activities are often out of context

·        Math has little personal meaning or relevance

·        Math remains something other people do

Culturally relevant approach

·        Math is a vital aspect of culture

·        Teachers stimulate students to create mathematical activities using situations and materials easily found in the environments where the students live. 

·        The teacher facilitates and extends students investigations. 

·        Students share their discoveries.

·        Multiple concepts are simultaneously explored as students invent their own procedures.

·        The result: students realize they possess an innate ability to think and become creatively involved in mathematical activities.  Math becomes something which surrounds them.  Math is everywhere and part of everything.

A.J.Bishop wrote in his book, mathematical Enculturation (1991, Kluwer Academic Publishers) that Mathematics occurs across cultures in six aspects of human activity.  No human culture has ever been without mathematics although frequently informal in nature.

1.     COUNTING – one to one correspondence - keep track of possessions

2.     MEASURING – comparisons according to attributes – common units for length, area, volume, weight, temperature, speed and time.

3.     DESIGNING AND BUILDING – shapes of buildings, tall, low, exploring for strength in structures, use of Lego in elementary school, explore patterns

4.     LOCATING – finding position, compass direction, points of reference

5.     EXPLAINING – Informally and formally making sense depends on organizing and interpreting data.  Graphs, diagrams, charts, tables e.g. TV viewing habits, fast food preferences, earth’s temperature, use of symbols in equations

6.     PLAYING – exploring informally – having fun.  Many games use a geometrical field such as a diamond, rectangle etc.  Many games involve chance – cribbage, solitaire, chess.  The mathematical concepts are prediction, strategic thinking and anticipation.

Examples in Native American culture where math is used in a culturally relevant manner the result being that math is one of the favorite subjects in these schools.

Mathematical and cultural insights associated with beadwork:

·        Choice of color and design

·        Shirley explains “when you do loom work, it is important to know that you always must string your loom so that you have an odd number of beads in each (horizontal) row.  This is because the median (bead) acts as the center point.  You need it to flip your pattern so that one side will mirror (reflect) the other.”

·        Counting and computation skills are very important in beadwork and the geometric patterns developed.

·        According to Shirley almost all mathematical concepts  in elementary school can be taught through beadwork – basic operations, measurement, perimeter, area, fractions, decimals, ratios, percentages, symmetry, geometry transformations – flips, rotations, slides.  Computer software can be used for design

·        “Beadwork teaches me organization, discipline and observation.  It makes me stop and look at things a little longer.”

·        The hand is man’s greatest tool. We have two of them that are identical.  So we can measure in two different places at the same time.  We can move them everywhere.

Developing Culturally relevant Mathematics Instruction and Activities

The basic developmental steps are:

1.     Interview Elders/cultural representatives who will describe a particular activity important to the tribal community.  One should seek not just content knowledge but also related beliefs, values and traditions related to the doing of the activity.  Elders often maintain a special respect in native communities and their words and presence can establish motivation as well as credibility for what is taught.

2.     The teacher examines the knowledge gained for curricular connections to the core standards.  A list is made of mathematical principles/concepts to teach.

3.     A lesson or series of lessons is designed around the concept or principle.  The lesson could contain physical, emotional, and spiritual objectives in addition to the usual cognitive objectives.  Information is presented using a variety of techniques but the main instructional emphasis should be on cooperative problem solving using materials/models and hands-on interaction.  The context of the culturally relevant application provides additional opportunities to share and discuss the values, beliefs and traditions inherent in the application.  Students should be encouraged to establish a personal understanding of what is studied and share their newly gained knowledge/wisdom in circles of sharing during the activity.

4.     Assessment is typically performance based.  Attitudinal as well as cognitive evaluation can be established.  The process a student has exhibited in the completion of an activity will often be as good if not better demonstration of learning as that of the final product. Primary in the learning is the degree to which the learner establishes personal meaning for use in ones life and for the benefit of the community.

The basis developmental steps are:

1.     Collect examples of Indigenous Cultural applications.

2.     Examine the applications for embedded concepts and principles

3.     Implement lessons – encourage individual meaning making

4.     Assess using a variety of techniques.

Brian Kane

Crow Creek High School

May, 2003