Mathematics

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Facilitator: Laura Monagan, Holton-Arms School

Notes from January 31:
 * __Session 1: Brainstorming Topics for Discussion/Why we're here:__**
 * 1) Transition Issues
 * 2) Curiosity
 * 3) Real World
 * 4) Integration
 * 5) Inside/Outside Classroom
 * 6) Steal Ideas
 * 7) "Special" Programs
 * 8) Age-appropriateness
 * 9) Scheduling
 * 10) Middle School girls
 * 11) Joy & Enthusiasms
 * 12) Teaching/Embracing Thinking
 * 13) Implementing STEM course
 * 14) Problem-based Learning
 * 15) Technology Access
 * 16) Reading Issues
 * 17) Faculty Ignition
 * 18) Curriculum Design
 * 19) Technology in Math
 * 20) Variety of Ability Levels
 * 21) Block Schedule for Math
 * 22) Computer Programming
 * 23) Vertical/Horizontal Integration
 * 24) STEM vs. Theoretical Math
 * 25) Integrating Tech Expertise
 * 26) Scope & Sequence/Benchmarks
 * 27) Ask for Science Top 10
 * 28) Discuss Best Practices
 * 29) Philosophical Questions
 * __Session 2:

Part 1: Developmental Expectations/Scope & Sequence/Benchmarks/Transition Issues/Age-appropriateness__**

1. In 7-10(concrete thinking years), are we asking kids to do things they are not ready for? 2. If we teach Geometry earlier, what course of study would the students then take after that? - Offer more classes to help weaker students have more options instead of just Calculus - Restrictions on what to name courses - whether or not the course is accepted by colleges (Discrete vs. Senior Topics) - Colleges find it a deterrent if students are not enrolled in math specifically and all core classes in their senior year of HS 3. Should the sequence be Algebra 1, Algebra 2, Geometry or Algebra 1, Geometry, Algebra 2? - SAT drives curriculum - Geometry has to be taken before exam which controls the order of courses - Integrated program helps to merge courses together at earlier times which ties material together and allows material to be covered before SAT exam at a comfortable pace 4. Should we incorporate Statistics into the Scope & Sequence - how to do this? - Trimester electives for 10-12 grades: Trig, Stats and Finance 5. Should all 8th graders take Algebra 1? - Depending on grade earned in course, may or may not be counted as a HS credit - retake in 9th grade 6. When is it appropriate to have students of different ages/grades in the same class? 7. Students hit a wall at different times - how to keep the "track" flexible and effective? - How to assess whether placement is appropriate? - Who chooses which track students are placed on? Parents? Teachers? Students? - Placement tests: How do you deal with parent reactions to performance on test? - Parent forms to be signed signifying agreement of school's placement - Summer work to prepare lower ability students for honors courses - helps parents to back off as well - Summer work to allow changing between tracks of courses to keep things flexible - Allow students to double up in math courses to get on faster track - Some schools don't track students - works well in lower grades: helps to encourage weaker students to open up more when placed in a class with stronger students - more difficult in upper grades: can't reference other courses (chemistry/physics) to relate material because students may not have the courses yet 8. Response from Science to our request for "Top 10" 1) Graphing a)  Understanding that they represent relationships between variables b) Best fit lines c)  Analyze the relationships in an equation d) Choosing correct type of graphs 2)  Communicate with science to collaborate topics/use common terminology/common techniques a) Visit each others classes 3)  Use science problems/word problems as examples in math class. (ie. Lose The Train Problem) <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">4) <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">Difference between a number and a measurement, Scientific notation, significant figures <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">5)  <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">Use variables other than ‘x’ <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">6) <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">Determine if an answer is a reasonable answer <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">a)  <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">don’t be a slave to the calculator <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">b) <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">Make reasonable predictions for answers before solving a problem <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">7)  <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">Unit conversion/unit analysis <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">8) <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">Simple statistics (error analysis) <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">9)  <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">The process of problem solving, not just the solution <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">10) <span style="FONT-SIZE: 14pt; LINE-HEIGHT: 115%; FONT-FAMILY: 'Times New Roman','serif'">Solving problems algebraically not just mathematically. **__Our Responses/Questions to Science Top 10:__** 1. Which science classes incorporate certain math topics (logarithms, graphing/best fit) and to what extent are these covered in science? 2. When covering math topics in a science class (proportions) it would be helpful for the science teacher to pause and revisit teaching that topic if students seem weak in that area rather than depending on math teacher to cover all math skills alone 3. Language used in math and science classes isn't the same and causes students to be confused 4. Course selection in science should be based on level of math skills so that we're covering same math topics in same year to reinforce relationships 5. History and English have tied curriculums together (studying american history and reading american literature at same time), how can math and science work this relationship out? Where find time to communicate together?

1. What interdisciplinary projects/courses is your faculty working on? - Physics/math trip to amusement park and projects are graded twice (once as a math grade and once as a science grade to get two different viewpoints) - Student poll from elections for government class and then statistics class took over and analyzed the data - 6th grade takes Chinese as a language and social studies is teaching asian cultures 2. What are the encouragements to interdisciplinary teaching/learning at your school? - Time is actually saved: use both class periods and get a double class period to work on project or take a trip 3. What impediments are there? How might they be overcome? - Easier for MS grades - time is more relaxed - Using joint projects in two classes allows more time for students to complete projects and lessens the time one class is impacted - AP courses have no time flexibility - All teachers are not on board with interdisciplinary lessons - pull one day out of rotation and make it an integration day for all courses - Being forced to integrate technology or some other aspect from administration that cuts into time for interdisciplinary lessons - Once school year starts, time to discuss is lost between teachers: can this be built into prof. development before school?
 * __Part 2: Interdisciplinary: LS/MS/US__**

1. Who are our students, really? 2. When have we been successful at inspiring our students to think? 3. What are we currently doing to help our girls overcome socially projected stereotypes about girls and math? About girls as mathematicians? 4. Best Practices in: - Collaborative Coursework: Problem based approach - work inside and outside of class with one another to solve a problem, girls discover on their own that working together helps them get to a solution faster and more easily, Peer edit/grading in math: students have to find mistake and explain it to their classmates rather than just grade for correctness, allow class to work together to solve a problem and allow each girl to contribute - Hands-on Investigation: Geometry (Build an open box/closed box to discuss and compare volume using same size paper- students came up with questions and relationships about volume size without teacher prompting, sketchpad, ratio and proportion - Barbie measurements vs real girl measurements, dice and probability - design own game using different dice to increase probability or make it fair, research topics - girls select 3 topics to turn in to teacher and distribute among students to do an oral presentation) - Encouraging Expertise and Control: have girls teach class and share solutions, math clubs that are student run to work problems, take pictures of conic sections around campus and share with class, peer tutoring programs, physical activity in problem solving to reinforce learning, Nike Plus with iPod to track movement and speed and graphs results on iPod and girls can figure out functions and increasing/decreasing, change in speed, etc. - Stressing Creativity: Identify and celebrate different problem solving strategies and approaches to a problem, allowing students to try and fail and find a new approach that works, have students talk out different approaches and explain why each one that didn't work failed and how it lead to another approach, "Crossing the River with Dogs" using lower level problems to see how girls try to bring upper level skills to solve - Using the girls' interests as a starting point for teaching math: how girls like to learn rather than basing curriculum around girls interest (easier in other courses like science), allow discussion time, group learning, give direct feedback, individual white board assessments, journaling - allows writing to be integrated into math and lets girls write about what they're interested in and can be used to help solve problem sets in class - Presenting math as a "helping field": Statistics - uses math to better life based on results (women and ovarian cancer relating to false positives) hiring practices of minorities in companies what are the factors?, Economics/Calculus - marginal revenue/profit, maximizing use of non-renewable resources, Geometry- logical thinking, Mathematics is a universal language - know to go into all different fields
 * __Session 3: Best Practices to Inspire Joy and Enthusiasm in our Students__**

Notes from February 1: __**Session 5**__ 1. Problems - Investigation based textbooks are problems because we can’t discover everything, have to tone down program - Can we still meet the minimal objectives required for the next course? - Have had to cut out some parts of programs to allow for more time - Need to restructure course for weaker students so that there isn’t so many topics being covered in one day – helps students stay involved and focused - A lot of time required the first year of teaching program (at least a semester ahead of students) to stay on top of program – problems aren’t easy to see where solution is going - No textbook to shadow program (some feel this is a good thing) - Larson book used to supplement (mixed results from students) - Traditional assessments don’t work well with this program – have to create own assessments that follow methods of program - Difficult adjustment for parents and students coming from a traditional program - focus on not defending program – just explain philosophically 2. Successes - Cut down extra-curriculum programs to make more time - 6 pages of problem solving (1 per page) per night, no previous knowledge required class next day is spent going over different methods of solving same problems - Girls become much stronger problem solvers through exploratory and reinforcing problems - Honors kids get to take control of class through these programs - Encourages students to use web resources instead of depending on a textbook - Resequence problems instead of supplementing with a textbook - Journals written by students used as reference books - Used as backbone for developing Geometry skills - Limit time students should be working on problems – if they’re working too long, they’re not getting the point of the problem solving program - Every problem gets discussed so weaker students feel more confident that they’re not the only one with a question on a certain problem – issue doesn’t arise
 * I. Problem Based Learning**

1. How laptops are being used in math classes - Geometer’s Sketchpad - Fathom – useful for graph analysis and very user friendly - Teachers have to be careful to not have too much already solved on computer, need to allow students to see how problems are being solved, not just the final solution - InterWrite pad - Tablet laptops help control students’ appropriate use in class – more difficult to hide - One Note program used – easily customizable and documents easily shared between teacher and students, great organizational tool - Maple - Girls have to buy a new laptop in 7th and 10th grade but was able to sell idea to parents with promise of students receiving tech support from school through college - Some schools have laptop leasing program 2. Graphing Calculators - TI SmartView – allows girls to see keystrokes 3. Are students learning skills or learning how to manipulate software? 4. Podcasts 5. Dino - Tested in some schools – really expensive so not supported by administration - Allows teacher to see all laptop screens in class and take control of their laptop, control what programs they can open, project student work on large screen for whole class, survey class anonymously and project results - CPS system is cheaper and allows some of the same tasks – immediate survey results
 * II. Technology in Math**

1. 8th grade – not all girls are ready for Algebra 1 - create a track at this point which allows more flexibility later on in tracking - if not split track early on, left trying to cover Prealgebra topics too late in maturity 2. Topics like fractions and graphing lines are taught too early and forgotten later on - spiraling techniques help reinforce topics throughout all topics - spiraling doesn’t require mastery at any given level, so topics are continuously retaught year to year 3. Expectations need to be the same for all teachers teaching same courses so that when students arrive at later courses, teachers can expect same knowledge to have been learned 4. Mixed grade level classes require a lot of social adjustment which isn’t always expected
 * III. Age-Appropriateness**

1. Consensus points - Importance of Problem Solving – encouraging creativity, risk taking and not being afraid to fail (or just not be perfect at something) - Active collaboration and communication cross curriculum at all levels (teachers/dept/admin especially within STEM teachers) - Wise use of technology as a tool – not a means to an end: availability, appropriateness, cost and usefulness issues - Not all students can learn these skills/tools the same way at the same time – spectrum issues and learning style issues - Balance of skills/conceptual understanding; traditional models vs. discovery based 2. Emerging themes 3. Where do we go from here? - STEM networking - Opportunities to see each other and how STEM courses are succeeding - Data and results of initiatives after workshop sharing – sharing what worked over the next year - Bring along less enthusiastic colleagues next year to get others to “buy in” - Integration of STEM beyond STEMers (branching out to other faculty) - Submitting lesson plans and curricular info on wikisite or other site for sharing - Increase participation of college administrators involved with engineering and other STEM fields
 * IV. Wrap-Up**

[|mrdardy] **** This word has already pooped up in the math conversation. The following link has a terrific essay discussing this idea in the classroom.

http://mail.baylorschool.org/~dkennedy/assessment

Jim Doherty Math Department Chair Kent Place School Summit, NJ