I'm taking some time off right now to do a Master's degree through Harvard Extension, and I'm also taking multiple classes through Coursera, EdX, Kennedy School ExecEd, UC Irvine, etc. Everything from educational policy & leadership to quantitative research & data analysis to non-profit management & financial accounting. This blog is a place for me to collect my learnings from this adventure I'm on! Most of the time, I'll just be cutting and pasting from various assignments or papers to be able to easily reference them later, but sometimes I'll do specific blog posts knitting my thoughts together from the different coursework. :-)

Tuesday, September 30, 2014

Logic Model for Nonprofit Financial Stewardship

Hi there, I'm in the midst of starting a nonprofit focused on early math learning.  The mission of the Early Math Initiative is to promote mathematical understanding and problem solving among young children with a special emphasis on low-income children ages 2-5 in the United States. The Early Math Initiative provides high-quality, one-on-one interactions with trained volunteer 'buddies' in early ed settings such as preschools or daycares, plus family support and in-home games & materials, to develop the critical early math skills, confidence, and joy, which young children need to be successful in school and in life.

Draft Logic Model -

Resources

* Volunteers for 1-on-1 interactions & game nights
* Research-based activities & games
* Connections with low-income daycares and preschools
* Connections with local colleges & businesses to recruit volunteers
* Funding for materials, online resources, & organizational support
* Space to hold family game nights
* Manufacturing capabilities for games & materials

Activities

* High-quality, 1-on-1 interactions between young children & volunteers in early ed settings
* Family support through game nights & take-home games/materials
* Volunteer training in early math best practices
* Online sales of games & materials on a 'one-for-one'/'Toms Shoes' model
* Online videos demonstrating 'math talk' in everyday activities

Outputs

* Number of volunteers trained and interacting
* Number of early ed settings (daycares, classrooms, etc)
* Number of children participating
* Number of parents attending game nights
* Number of games sold online
* Number of online video views and interactions

Outcomes

* Children have higher early math skills at end of program
* Children report enjoying math, feeling competent, and seeing math as useful
* Children enter Kindergarten with higher readiness skills
* Parents engage in more 'math talk' and games at home
* Parents report feeling more positive about math & their own problem solving abilities
* Volunteers report more connection to their community and more awareness of how math is all around us

Impact

* Children maintain higher math skills, confidence, & enjoyment through elementary and high school, including higher academic grades
* Children graduate high school at higher rates
* Children attend college at higher rates
* Children have better career and financial success in adulthood


1) What are the key lessons and insights you have about your organization’s financial resources as a result of developing your draft logic model?
One of the insights I got through doing the logic model was actually more about human resources - many of the resources we need to do the activities can be achieved through a combination of finances and human capital.  Certain things have to be 'bought', but other aspects could be found or 'traded' through connections.
Looking through the outcomes and the impact also reminded me to focus resources (financial and otherwise) on the activities that do show the results that we're looking for.

2) Did any parts of your logic model surprise you? Which ones and in what ways?
Working through the logic model short-term outcomes surprised me to think about what else are we hoping to see besides just raising test scores, and then how will we measure those outcomes (how do you measure enjoyment of math?).  Also, the children are important, but we want to see change for the parents/families and for the volunteers as well.

3) Are there any action steps concerning your organization’s financial resources as a result of developing your draft logic model? What do you hope to accomplish by pursuing these action steps?
At this point in the start of the nonprofit, we're mostly looking for funding, so clarifying our logic model is wonderful to be able to better articulate to potential funders what impact we're going to have.  I will start including the full model in larger fundraising, and mentioning the key aspects in smaller fundraising.

Wednesday, September 24, 2014

Week 3 Post for Educational Policy - Desegregation

 Prof Peterson describes the Brown decision as "the signal accomplishment of the 20th century as it transformed opportunity for Black Americans and created the opportunity to create a more egalitarian society consistent with the nation's ideals" (Desegregation III, 9:00mins). Although that decision resulted in both primary and secondary accomplishments for Black Americans, the benefits were not as drastic and immediate as many had hoped at the time. Today, the U.S. still cannot claim racial equality in student achievement and attainment outcomes.

Please describe some of the primary and secondary accomplishments that are associated with the Brown decision. Further, what policies or constitutional changes should we now pursue to realize the goals of racial equality in educational outcomes? Make sure to acknowledge potential implementation challenges that might accompany your proposed policies (such as the interracial violence that erupted in response to forced busing in the 1970s).

Example 1: TA Anna evaluated the effectiveness of a statewide voucher program in its effectiveness at reducing racial stratification in Louisiana's public schools. What's your evaluation of this proposal to use school vouchers as a tool to better integrate both public and private schools? Is that goal worthy in and of itself or should we be more focused on improving test scores of minority students? http://educationnext.org/the-louisiana-scholarship-program/

Example 2:  TA Anna also evaluated the effectiveness of teacher-student race matching as a strategy to improve minority students' achievement outcomes. She finds positive, statistically significant achievement effects when Black and White students are assigned to race-congruent teachers in reading and for Black, White, and Asian students in math. What's your evaluation of this proposal as a way to close persistent achievement gaps? http://www.uaedreform.org/representation-in-the-classroom-the-effect-of-own-raceethnicity-teacher-assignment-on-student-achievement/ 


As Prof Peterson describes in the videos, the Brown decision that 'separate but equal' was unconstitutional was definitely a turning point.  Not everyone agreed with the ruling and some schools were closed down rather than be desegregated.  But on the whole, the Brown decision fueled the civil rights movement, and the Civil Rights Act of 1964 also helped to move the desegregation forward.  However, interracial violence was still prevalent, especially around 1968 with the Watts Riots and the assasinations of Martin Luther King Jr and Robert Kennedy.  In the Milliken versus Bradley case in 1974, the courts decided that de facto segregation was ok, as long as de jure (or explicit law) segregation wasn't happening.  This distinction has led within district segregation to go down over the years, but between district segregation to go up.  Within districts, black and white students attend the same schools and aren't segregated, but black and white families often choose different places to live, and thus the school districts are often segregated in black districts and white districts.

While the Brown decision has had a huge impact, we still have significant racial inequality in educational achievement.  Part of this may be because of the between district segregation - but how do we integrate different ethnicities?  In the past, bussing has been tried - but people often prefer to go to schools closer to where they live, and is it really the best use of the children's time to have them in transit for hours each day?  Perhaps giving families a choice of schools would be the best option?  But as the All Over the Map reading (http://educationnext.org/all-over-the-map/) brings up, poor families often don't have the ability or the information to adequately evaluate schools in order to make the best educational choice - or they may value other aspects besides high quality instruction, such as proximity to caregivers or maintaining previous school community connections.  And even if schools start to become more integrated, there are often major cultural clashes as the Elephant in the Classroom reading (http://educationnext.org/the-elephant-in-the-classroom/) points out.  Different ethnic groups and social classes sometimes have different ideas of what school should be like, and how teaching should happen.  I've done some reading about KIPP schools, which can seem very strict to educators more accustomed to progressive teaching methods - but after the Elephant in the Classroom article, I have a better sense of how KIPP's culture fits in with the culture of the students it's trying to serve.

But what do we need to happen in order to achieve racial equity in education?  The Lousiana Scholarship program shows that at least in some situations, school choice can result in better integration.  While I would argue that integration is a worthy goal for helping students to have a broader perspective and to open up their filter bubble (the LSP article made me more aware of the filter bubble I live in - I had no idea that the government was still monitoring schools for compliance with desegregation laws), I would want to see data on whether the integration actually improves educational outcomes.  If integration means more students attending high-quality schools, then my guess is that there would be higher educational equity, but if integration just means moving students around within low quality schools, then even if there's more equity between ethnicities, it wouldn't work if that equity point is low.  The goal is not just to be equal - it's to have everyone achieve higher.

The Representation in the Classroom paper in some sense argues against integration, because if students learn better in classrooms where their teacher is the same race or ethnicity, then maybe we should segregate all students into black classrooms and white classrooms with the appropriate teacher?  If this would actually result in consistently higher academic achievement, then perhaps it is an option to be made available to families, in a similar way that some schools are all-girls or all-boys.  Although I do wonder if only learning one cultural norm may have negative future effects. Students especially in this day and age need to know how to deal with all different types of people in order to move forward professionally.  Perhaps if we had high-quality teachers in integrated classrooms who had high expectations for all of their students, no matter what race or ethnicity...

Sunday, September 21, 2014

Week 2 Post for Saving Schools

Based on the lecture videos and required readings for this week, discuss what you feel the role of the local school board should be in the 21st century.

The Lost at Sea reading does bring up some good points about who might be on school boards, and the various agendas they would have.  This reading as well as the video also talks about how while school boards are elected, they're elected by such a small minority of people that it's not really participatory democracy at work.  Like any system or set of organizations, some of them are going to work extremely well, and some not as well.  To say that we should do away with school boards because some of them aren't very good is not a solution.

I think we still do need some local accountabilty and a system of checks and balances.  Having a school board that can look over the schools and provide some outside perspective is important.  As the Steering a True Course reading notes, some school boards are pushing for educational reform and establishing even more rigorous accountability measures than the state.  And the same reading talks about how there still need to be financial oversight.

I see the role of local school boards as providing more accountability and oversight, and giving the local community a way to participate in the schools.  Now that we have more professional administration (superintendents, etc), the school board doesn't need to be involved in the running of the schools, but rather should be more a board of advisors who can look at the overall picture and help with strategy.  We don't need people who are just going to say yes to various measures that the administrators are already doing, we need people who can help the administrators plan and change in order to better serve the students.

Saturday, September 20, 2014

Assignment 2 for Social Entrepreneurship - Logic Model, Beneficiary Experience Table, and Deliverables Table

I am working on a social enterprise supporting early math learning for preschool children in the US.  I've attached the logic model for our initiative.



Our Beneficiary Experience Table... from the perspective of family of the preschool child
- enroll child in preschool that is participating in the program
- hear about the family math nights from the preschool and our program
- arrange to have the evening available
- find transportation to the school
- attend the family math night
- be instructed in how to play the games
- bring the early math games home
- find time to spend with child
- play early math games during that parent-child time


Our Beneficiary Experience Table... from the perspective of the preschool where the child is enrolled.
- hear about the early math initiative
- connect with our program and arrange to be a participating school
- create time in the school day for the volunteers to come in and play games with the children
- find a suitable time and location for the family game nights
- coordinate with our program for the family game night logistics
- support the volunteers in interacting with the families during game night
- maintain contact with the families to support continued use of the early math games at home


Our Deliverables Table...
- Collect the research about which games are most effective
- Create the curriculum and actual game materials
- Market and use social media to reach out to preschools and families to participate
- Recruit volunteers to go to the preschools and to do family game nights
- Train the volunteers in using the research-backed games
- Coordinate the logistics of the volunteers going to the preschools
- Coordinate the logistics of the family game nights
- Follow up with preschools and families to encourage continued game playing
- Create online videos of best practices in early math activities

Project Proposal for Coursera Data Analysis

In the Data Analysis Coursera class, we get to do a project based on a research question and data that we choose!  So even though it's a math/there's only one correct answer type of class, I can post some of my work since it's about the data that I'm choosing rather than everyone using the same data.  (I still want to write a post about what I can and can't post here because of whether or not the homework has 'one' correct answer.)

RESEARCH QUESTION: In one sentence, what is your research question?
Is there a relationship between educational achievement, as measured by highest degree, and hours of TV watched per week?

DATA - Citation: Include a citation for your data, and if your data set is online, provide a link to the source
I will be using the General Social Survey dataset as provided for this class - I'm going to be using only the data from after 2000 in order to try to make the results more generalizable to current day.
http://bit.ly/dasi_gss_data

DATA - Collection: Describe how the data were collected.
The data for the General Social Survey has been collected through interviews every year or two since 1972.  From the intro pdf at http://publicdata.norc.org/GSS/DOCUMENTS/BOOK/GSS_Codebook_intro.pdf, "Each survey from 1972 to 2004 was an independently drawn sample of English-speaking persons 18 years of age or over, living in non-institutional arrangements within the United States.  Starting in 2006 Spanish-speakers were added to the target population."  The exact sampling procedure has varied over the years as described in http://publicdata.norc.org:41000/gss/documents//BOOK/GSS_Codebook_AppendixA.pdf

DATA - Cases (observational/experimental units): What are the cases? (Remember: case = units of observation or units of experiment)
The cases are individual adults - English-speaking, 18 and over, not living in institutions; with Spanish-speaking adults added for surveys done 2006 and later.

DATA - Variables: What are the two variables you will be studying? State the type of each variable.
I will be looking at...
1) educational achievement as defined by highest degree - DEGREE.  In the GSS data, it's an ordinal/categorical with five levels (Left HS, HS, Junior College, Bachelors, Graduate), so I may break it down into two or three categories, such as High School vs College, depending on the statistical methods we learn and if I can compare that many levels.
2) hours of TV watched a week - TVHOURS.  It's numeric with values from 0-24.

DATA - Type of study: What is the type of study? Is it an observational study or an experiment? Explain how you've arrived at your conclusion using information on the sampling and/or experimental design.
The GSS Study is an observational study - the interviewers 'observe' or take note of the participant's answers.  There's no treatment or control groups, so it's not an experiment.

DATA - Scope of inference - generalizability: Identify the population of interest, and whether the findings from this analysis can be generalized to that population, or, if not, a subsection of that population. Explain why or why not. Also discuss any potential sources of bias that might prevent generalizability.
The GSS Study hopes to represent the whole US population - or at least English (and now Spanish) speaking adults.  Because it's an observational study, it has external validity and can be generalized to the population of interest.  The study tries to get a representative sample through its surveying method, although the method has changed over the years of the survey.  One thing to note is that the survey answers collected from many years ago may not generalize to the current population (although that data would probably accurately reflect the population of that time), hence why I am only using the data from after 2000.

DATA - Scope of inference - causality: Can these data be used to establish causal links between the variables of interest? Explain why or why not.
No, these data cannot be used to establish any causal links between the variables.  Because it's an observational study, and not an experiment, we can only tell if the two variables are correlated - and correlation does not equal causation!  In this particular case of education and tv watched, I'm not even sure if causality is really something to think about.  The educational attainment came first, so therefore does going to school longer cause someone to watch less TV?  Or is it more likely there's a confounding variable of motivation or intelligence or something else that causes both higher educational attainment and less TV watching?


EXPLORATORY DATA ANALYSIS:
Perform a brief exploratory data analysis - just one or two relevant descriptive statistics and visualizations of the data. Also address what the exploratory data analysis suggests about your research question.

Using the GSS data from after the year 2000, I found that the mean hours of TV watched was very different for the different levels of educational attainment.  The overall average hours was 2.983, but the average for the different education varied from 1.939 to 4.070, indicating that there is a relationship between education and tv watched.

I also did a boxplot to see the distributions over the different educational levels (attached as a pdf).  The distributions seem to be fairly similar, with long trailing tails of outliers going toward the maximum of 24 hours per week.  The boxplot shows that the median for left high school and high school is the same (3 hours), and the median for junior college, bachelors, and graduate is the same (2 hours), so perhaps the greatest difference is between the two broader categories of 'high school or lower' and 'any college education'
.

by(gssafter2000$tvhours, gssafter2000$degree, mean, na.rm=TRUE)
gssafter2000$degree: Lt High School
[1] 4.069703
---------------------------------------------------------------------------- 
gssafter2000$degree: High School
[1] 3.169679
---------------------------------------------------------------------------- 
gssafter2000$degree: Junior College
[1] 2.641186
---------------------------------------------------------------------------- 
gssafter2000$degree: Bachelor
[1] 2.230769
---------------------------------------------------------------------------- 
gssafter2000$degree: Graduate
[1] 1.939353



jklj;




Wednesday, September 17, 2014

Post for Ed Policy - Methodological Thoughts

One of the most policy relevant charter school studies is an observational study conducted by the Center for Research on Education Outcomes (CREDO) at Stanford University. This study has high external validity. (Information on their methodology can be found at http://credo.stanford.edu/documents/NCSS2013_Technical%20Appendix.pdf, pages 5-11, which also discusses the internal vs. external validity concerns discussed above. The main report (http://credo.stanford.edu/documents/NCSS%202013%20Final%20Draft.pdf) also discusses the methodology on pages 8-11, but in less detail.)
CREDO matches each charter school student to public school students from “Charter Feeder Schools” that have similar baseline test scores and the same race, gender, special education status, limited English proficiency status and free lunch status. They then compare how the charter school students perform on low-stakes tests relative to public school students.

 Overall, I was very impressed with the amount of data they were able to collect and process, although when analyzing that many different sections and doing so many statistical analyses, they're bound to find some significant results.  They do seem aware of this, mentioning it in the issues associated with repeated tests - although also mentioning that they chose not to reduce the significance level, even with so many tests.  Given this, we have to look a bit more carefully what is 'significant', especially since so many of the results they found were within .01 standard deviations, at least when aggregating all of the data nationally.  Also when matching the VCRs, they did allow variation in the TPS students' starting scores of plus or minus 0.1 SDs - which is often more than the level of difference they're often finding.  They do talk that not having exactly equal starting scores, and seem to feel like it's not an issue once averaged out - but to a less statistically trained eye, I wonder. 

And while talking about the VCR matching, I'm also wondering if the charter school students are going to show more variation than the VCRs, because each charter student is matched with an averaged VCR including up to 7 TPS students.  The score of one is going to show more variance than an averaged score.  Again the study does mention this criticism, as put forth by Hoxby, but says that they did more statistical analysis to find that it wasn't a valid criticism.  Another interesting point to me was that the matched TPS students had a lower than average change, meaning that the virtual twins did not progress as much as an average student.

On the issue of confounding variables - Because this study wasn't looking at lottery 'winners' and 'losers' who had all tried to get into the charter schools, the main confounder that stuck out to me was around parent involvement and school choice.  The charter school students were matched to TPS students on the basis of  race, gender, free or reduced price lunch status, special education status, and English language learner status.  But what about the parents?  The VCRs came from feeder schools where presumably all of the parents knew about the charter schools, and yet only the parents of the charter school students actually enrolled them in a charter school.  The analysis states that the VCR method produces results that are not significantly different from experimental methods, and it also points out some issues with using lottery as an experiment (not totally random, not enough students, etc), but I still felt like the difference between who chooses to attend charter schools versus who doesn't would be a large confounding variable.  Not sure which way it would affect the results though.  Perhaps parents who are more involved would choose charter schools, and their children might do better because their parents are involved and supportive of their education?  Or perhaps parents whose children aren't doing well in TPS are more likely to move to a charter school?  (The study did mention some evidence of this.)  Or perhaps parents who have a higher education level are more likely to research and enroll their children in a charter school, and parental education level tends to correlate with student achievement?

Other possible confounders... Do charter schools attract better (or worse, or newer, or...) teachers?  Perhaps any effects are from differences in teacher quality.  Do charter schools have different class sizes, or school sizes?  I think the study mentioned that charter schools were often smaller schools than the TPS (although I can't find the reference now that I'm looking again).  Do charter schools have more instructional time?  Some charter schools have longer school days or longer school years - maybe those '7 extra days in reading' results actually came from having seven extra days of instructional time.  Do charter schools have a stronger school community?  By choosing to go to a school, students might be more engaged with the school community, which may affect math & reading scores.  There are a lot of potential differences between charter school students and TPS students that were not accounted for in the VCR method.  Thus the results probably cannot be externally valid for all students.

Another big issue that stood out for me was the wide variation in the state scores - and most likely in individual school scores.  Charter schools are not a homogenous group, and so to make judgements based on aggregate might not be very helpful.  Just because charter schools as a whole are showing basically the same (or possibly a little bit better) results than TPS, tells you nothing about the charter school down the street from you, or even the charter schools in your state.  The study does delve a bit into the state differences, but I would have liked to have seen more.  I care less about the overall state of charter schools and more about which ones are working and which ones aren't.

Tuesday, September 16, 2014

Intro for Immunity to Change

Hi there, my name is Teresa Gonczy, and I'm an entrepreneur and educator.  Although currently I'm taking some time off to get a masters degree in education.  Because all of the classes I'm taking are online, I'm actually traveling a lot this year - mostly between Los Angeles, San Francisco, Chicago, and Boston.

By taking this course, I'm hoping to gain some insight into how I'm holding myself back, and then be able to change and move forward.  I'm not sure yet what goal I want to work on - I'm debating between some more personal goals, such as finding a spouse and starting a family, or more professional goals, such as leading larger organizations and going from having a local impact to a broader impact.

Looking forward to changing along with everyone over the next weeks!  :-)

Intro for NonProfit Financial Stewardship

Hi there, my name is Teresa Gonczy.  I'm an entrepreneur and educator who is starting a new nonprofit focused on early math learning.  I am also on the board of directors for a STEM education nonprofit with programs on the east and west coasts.  Previously I was on the founding board of directors for a charter elementary school in San Diego and for a family-friendly makerspace in Los Angeles.  I have a basic knowledge of general financial management from running my own businesses, but am less familiar with the specific rules and regulations around nonprofit financial management.

I am taking this course because as a previous board member, I've seen nonprofits struggle with finances, and I want my new nonprofit to start off on the right foot.  I also want to be able to advise the current nonprofit board that I'm on, as well as any future boards that I sit on.  I do have a fundamental understanding of bookkeeping and financial statements, so my personal learning agenda is mostly around making sure I know the specific fiduciary requirements for nonprofits.  I'll also be interested in working with constrained resources, since most non-profits are in that situation!

As I am starting a new nonprofit, the key challenges right now are getting funding, getting the books and initial forms set up correctly, and forecasting future costs to create a breakeven analysis.

I'm looking forward to 'meeting' everyone else in the course!

-Teresa :-)

**********************************************
Teresa Gonczy
Entrepreneur, Educator, Cognitive Scientist, Dancer

teresaeg@gmail.com
www.teresaeg.com
www.linkedin.com/in/teresagonczy/

Teaching Arithmetic HW#2


Problem 1 – Part a) The 'magic' trick involves choosing a single digit number (by picking an item and using the number of letters in its name), multiplying by 5, adding 3, multiplying by 2, and then adding a second single digit number. Then by subtracting 6, you can find the two original numbers – the tens digit will be the first number, and the ones digit will be the second number.

From an algebraic perspective, the whole ordeal boils down to 2(5x + 3) + y, which simplifies to 10x + y + 6, where x is the first number and y is the second number chosen. Hence after subtracting 6, it becomes 10x + y, so as long as x and y are single-digit numbers, this is the same as a two digit number with x as the tens digit and y as the ones digit. To explain this to a 6th or 7th grader, I would walk them through each step...

* pick x
* becomes 5x
* becomes 5x + 3
* becomes 2(5x + 3) = 10x + 6 – this step would probably take extra time to show how the two ends up multiplying to both the original 5x and the plus 3, to become '10x plus 6'. Might have to work through several numerical examples to help show the distributive property, while pointing out that number is always six more than the original number times ten.
* becomes 10x + 6 + y
* then we need to subtract six to get 10x + y
* 10x + y gives us our two original numbers – depending on the student's understanding of place value, this step might also take some extra explaining to help them see that the tens digit and the ones digit of a two digit number can also be represented as 10x + y

Problem 1 – Part b) So if we want to change the 'magic' trick so that we need to add 8 at the end, rather than subtract 6, then we want our final equation to boil down to 10x + y – 8. Working backwards, then we need the intermediate equation to be 2(5x – 4) + y, so in the telling of the trick, we would need to have the person subtract 4 in the middle, instead of adding 3.




Problem 2 – My own math magic problem! Blatantly stolen from... http://www.pedagonet.com/Maths/missingnumber.htm

Have your subject write down a number, at least four digits long. Then have them add up the digits in their number, and subtract that amount from their original number. Now in this new number, they cross out one of the digits, any digit. Then they tell you what the number is without the digit they crossed out (the webpage says to have them slowly read you the digits, but I think we can manage fine if they tell us the number, plus then it's less obvious that you're doing something with the digits). In your head, add up the digits off the number they give you and figure out what you would have to add to get to the next multiple of nine. That's the digit that they crossed out!

Example... first number 13579. Digits add up to 25, so we subtract 13579 – 25 to get 13554.
Now cross off a digit in 13554 to get 1554. The digits of 1554 add up to 15, so we would need 3 to get to 18 (the next multiple of nine). Hence your friend crossed off a 3. You found the secret number! :-)

But why does it work? (which is not explained on the website I stole the problem from)

1) Whenever you add up the digits of a number and then subtract them from the number, you'll get a multiple of nine. Why? Because of powers of ten and place value. Let's say we have a number with digits a, b, c, d, e – then the number could be seen as 10000a + 1000b + 100c + 10d + e. So if we subtract off the sum of the digits, we get 10000a + 1000b + 100c + 10d + e – (a + b + c + d + e) or 9999a + 999b + 99c + 9d, which will always be divisible by 9. (I figured this out with help from google and http://mathforum.org/library/drmath/view/62561.html)

2) Now that you have a number that's divisible by nine, the sum of its digits will always be divisible by nine, because of the magic power of nines! I've known this particular 'trick' for a while, but never really thought about why it works. So more googling... http://mathforum.org/library/drmath/view/67061.html

If we have a number with digits a, b, c, d, e that is already divisible by nine, then by place value, again we could see the number as 10000a + 1000b + 100c + 10d + e, or we could also think of it as (a + 9999a) + (b + 999b) + (c + 99c) + (d + 9d) + e, or as (a + b + c + d + e) + (9999a + 999b + 99c + 9d). So the original number (which is divisible by nine) is the sum of the digits plus a number divisible by nine. If we rearrange the 'equation' to get, we get that the sum of the digits equals the original number (which is divisible by nine) plus another number divisible by nine. We can factor out the nine from those two numbers to see that the sum of the digits must also be divisible by nine.

3) So we have a number that we know is divisible by nine, and hence the sum of its digits is divisible by nine, then if we don't add in one of the digits (the secret number), we can figure it out by seeing what we would have needed to still add in order to get a multiple of nine.





Problem 3 – The alphanumeric puzzle!
I enjoyed doing these types of problems as a kid in the book - http://en.wikipedia.org/wiki/Sideways_Arithmetic_from_Wayside_School

The book had some problems with numbers written as words, where it would work out to another number (written as a word), but I can't remember any of them now, so I used the app to come up with...

ONE + THREE = HIPPO

Ok, let me try to solve it without using the app...
THREE
+ ONE
HIPPO


So first some observations...
* E + E = O so O is even.
* There needs to be a carry over onto the T, so that T + carry = H (because if there was no carry, then T would equal H, which we can't have). And there also needs to be a carry over onto the H in three, so that H + carry = I for the same reason. And in the addition of two numbers, the largest (and only) carry we can have is one. So T + 1 = H and H + 1 = I, and thus T + 2 = I. Or we can think of T, H, and I as consecutive numbers.

Let's try some possibilities...
* E can't be 9, because if E was 9, then 9 + 9 = 18, O = 8 and carry the one, then 1 + E + N = P,
or 1 + 9 + N = P, but that's 10 + N = P, which would make N & P be the same digit (and carry the one), but each letter is a unique digit, so E can't be 9.
* What if E equals 8? Then O = 6.
* What if N equals 9, then P would be 8 – but E is already 8, so NOT CORRECT
* What if N equals 7, then P would be 6 – but O is already 6, so NOT CORRECT
* What if N equals 5, then P would be 4, and then 1 + R + 6 = 4 (or rather 14), which makes
R equal 7. But then H, I, and T end up being small numbers, which won't result in two carries.
Hmm... maybe I need to try large numbers for H, I , and T. Oh yeah, in order for there to be that second carry, H has to be 9 – duh.
* Ok, H = 9, so then I = 0, and T = 8. So far we have...
89REE
+ ONE
90PPO
* Let's go back to trying values for E... E can't be 9 or 8 because H & T are 9 and 8.
* What if E equals 7? Then O = 4.
* What if N = 6, then P would be 4 – but O is already 4, so NOT CORRECT
* What if N = 5, then P would be 3, then R would be 8 – but T is already 8, so NOT CORRECT
* What if N = 3, then P would be 1, then R would be 6... I think that works! :-)

So T = 8, H = 9, R = 6, E = 7, O = 4, N = 3, P = 1, I = 0
89677 + 437 = 90114 YES!
Problem 4 – Which is bigger, cube root of 24 or the fraction 10/3?
* Well, the cube root of 24 is going to be a little bit under 3, because 3 cubed is 27. And 10/3 is over 3 because 9/3 would be 3. So therefore 10/3 > (24)^(1/3)
* Or we could think about getting fractions with common denominators. To make the cube root of 24 into a fraction with three on the bottom, we need to multiply the top and the bottom by 3. So then we can just compare the tops of the fractions – which is bigger, 3*cube root of 24 or 10? The cube root of 24 is less than three so 3 times less than three will give us less than nine. And ten is bigger than nine, so again therefore 10/3 > (24)^(1/3)
* Or if we don't like having a silly cube root, then we can cube both of the numbers (since neither one is negative, we'll be ok in keeping the same number bigger even after we cube). So now, which is bigger, 24 or (10/3)^3? Well, (10/3)^3 is 1000/9, which is kinda a yucky fraction still. We could do some quick long division, and get about 111, which is a lot bigger than 24, and hence again therefore 10/3 > (24)^(1/3)

Problem 5 – What is two?
We often think of two as referring to two of similar objects. When we're first having kids learn to count, we place two crackers in front of them, and say “one, two... two crackers”. But two can apply to all sorts of different objects – and the two don't have to be similar. We can have 'two things', which are not similar, except in their thingness. And children have to learn that the two objects are still two, even if we move them around or change the objects to different objects.
Two is also the number that comes after one, and the number that comes before three. Some children first learn the rote counting without the actual correspondence to physical objects, and for them, two is just the second syllable in the verbal string that they sing when asked to count to ten... 'onetwothreefourfivesixseveneightnineten'.
Two can also apply to two groups of objects, such as when kids start to learn multiplication. Here, the total is much more than two objects, but we can divide the objects into two groups – and we could also start a discussion about evenness. Or a discussion of fractions... 4/2 = 2, 8/4 = 2, etc.
Two can also be a measurement - a counting off along a continuous dimension, rather than a counting of two discrete objects. Then we start thinking of where two fits in with decimals – it's not just bigger than 1, it's bigger than 1.9.
Two can also be a numeral. In base ten, it can represent 2*10 in 320
Problem 6 – Part A - One of your students can't understand why division by zero is undefined. He thinks 0 divided by 0 should equal 0, explaining that "if you have nothing and you divide it by nothing, then why don't you end up with nothing?"
* But maybe 0 divided by 0 should equal 1, because don't we 'know' that any number divided by itself is one?
* Or what if we let 0/0 = x, then if we move things around, we get 0 * x = 0. So x could be 3 or 4 or 10 million or pi – we could put any number in and zero times the number would equal zero. So therefore 0 divided by 0 equals all numbers?
* Or what if we think of division as repeated subtraction? Eight divided by two can be thought as how many times do you need to subtract two from eight to get to nothing. So how many times do you need to subtract zero from zero to get to nothing? True, zero times works, but so does once, twice, and any number of times. So again we get 0/0 equals any number?
So we call 0/0 undefined and indeterminate because we can't determine the answer.


Problem 6 – Part B - Another of your students says that not only is zero an additive identity (i.e. that zero plus any number gives you back that number), but that zero is also an identity with respect to subtraction.
* The student is correct in that zero subtracted from any number results in the same number, just as in the additive identity where zero added to any number results in the same number. Although we don't usually talk about a subtractive identity. Perhaps because subtraction can be thought of as addition of a negative number? So subtracting zero is like adding a negative zero? But what does negative zero mean? Or maybe we don't talk about a subtractive identity because the subtraction is not commutative? A + B = B + A, but A – B doesn't equal B – A. So A + 0 = 0 + A, but A – 0 = A while 0 – A = -A.

Interestingly, some of the early math research does refer to A + 0 = A as the subtractive identity...




Problem 7 – Reaction to article...
http://www.thephora.net/forum/archive/index.php/t-61001.html

Coming from a cognitive science/education/language background, I knew most of the experiments mentioned in the article, although hadn't heard of that particular culture. The log-linear aspect of learning is actually very important in early math, and seems to be a predictor of math ability - “Moreover, those children who were able to correctly estimate numbers' positions tended to score higher on the math portion of the Stanford Achievement Test, Ninth Edition.” http://www.apa.org/monitor/nov05/linear.aspx
Research shows that playing board games can help to move young children from log to linear...
And it works better if the teacher/parent helps the child to use 'counting on' language...

I was away on a camping vacation right before the fall term started – away from internet & technology, away from society, away from numbers – at least in some ways. Like the indigenous people, I told time by the sun – if a friend asked what time it was, I said morning, midday, afternoon, evening, or night. I didn't do much counting, but I also didn't feel like I was being 'productive'. Obviously we need numbers to function in the society that we have now – numbers are needed to create the words that I am typing on this screen, although in some sense, it's all zeros and ones, so maybe we don't need the higher numbers? :-)

Monday, September 15, 2014

Assignment 1 for Social Entrepreneurship

Signature Track:
  • Build a mind map AND a problem/solution statement for the project you will work on the next 6 weeks.


The problem I'm looking to address is inadequate school readiness skills upon entering kindergarten in the US. 45% of children live in low-income families - that's over 32 million kids (1), mostly in urban areas.  Many of these children do not have the basic pre-academic skills that they need to do well even in elementary schools.  At four years old, children below the poverty line are 18 months behind the normal development for their age (2).  Many early intervention programs focus on early literacy and language, but research shows that early math skills are actually more predictive of later academic success (3).

In general, low-income children fall behind because their parents don't engage with them as often in high-quality interactions.  Children from low-income families hear, and thus learn, about one third of the words as children in higher-income families (2).  Similarly with early math activities, low-income parents engage their children in far fewer math activities, and low-income children don't play nearly as many board games as higher-income children (4).  What if we could get parents playing these games and engaging more with their young children?

My solution would be to create new early math board and card games based on the research showing which games are most effective for teaching basic number sense concepts (4).  We would then sell these games through a one-for-one model, like Tom's Shoes, where every game purchased by a family that can afford it funds a game for a family that cannot afford it.  But I don't expect parents to magically change their behavior if we just give them the games.  That's where the service side of the equation comes in.  Volunteers will go into low-income preschools to play the games with the children in the classroom, and will also hold family game nights where the parents can come get their free games and learn more about how to engage with their children.  We will monitor the children's skill levels and survey parent participation, and add in more to the service side if the families need it.


(1) http://www.nccp.org/topics/childpoverty.html, http://www.nccp.org/publications/pub_1049.html
(2) http://www.nccp.org/publications/pub_695.html
(3) http://news.uci.edu/features/kids-skilled-early-in-math-do-better-in-school/
(4) http://www.psy.cmu.edu/~siegler/sieg-cdper09.pdf


Mindmap created using www.mindmup.com

Sunday, September 14, 2014

Forum Post for Saving Schools - US vs International

Read "U.S. Students from Educated Families Lag in International Tests" by Eric A. Hanushek, Paul E. Peterson, and Ludger Woessmann from the Fall 2014 issue of EducationNext:

"U.S. Students from Educated Families Lag in International Tests" - http://educationnext.org/us-students-educated-families-lag-international-tests/

Based on the results of this study and this week's lecture, are you surprised to discover that the United States has two large gaps in its education -- the gap within the country and the gap internationally?


I was not surprised to (re)learn about the two gaps - I'm familiar with both of them.  What was surprising to me was the first two charts - Massachusetts and Minnesota are highest for all students, but then when you look at students with low parental education, those two states are further down the list.  And Texas jumps to the top (from being 14th on the total list).  To me, that seems to indicate that Massachusetts and Minnesota schools may not actually be all that good - they just have good students to start with, students who have supportive learning structures elsewhere in their lives.  I would be much more interested in looking at the Texas school system to see how they're raising scores for students who come from less educated backgrounds.

Forum Post for Saving Schools - Ed & Economics

Read "Education and Economic Growth" by Eric A. Hanusehk, Dean T. Jamison, Eliot A. Jamison, and Ludger Woessmann from the Spring 2008 issue of EducationNext:

"Education and Economic Growth" - http://educationnext.org/education-and-economic-growth/

Based on this reading and the other material presented in this week's lectures, are you convinced by the evidence that there is a strong connection between education and economic growth?

As the article mentions, education is not the only factor in economic growth (having an open economy, etc are also important), but education does seem to be a strong factor.  I was glad to see that the research tried to separate out educational attainment (years of schooling) from cognitive skills (abilities actually learned), because just going to school is not enough.  Children (or adults) actually need to taking in the information and then able to apply it to new situations.  And sometimes that learning happens outside of a traditional school - for example, this EdX course!  :-)  I've seen some other research suggesting the goverance and health measures also mediate the education/intelligence effect - https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CB4QFjAA&url=https%3A%2F%2Fwww.aeaweb.org%2Faea%2F2014conference%2Fprogram%2Fretrieve.php%3Fpdfid%3D321&ei=KDUWVN7uE6GA8QHRn4G4Aw&usg=AFQjCNHnFN8WzabG1y_WxFeH3zKAxrDJcw&sig2=16sy5KQwoFDuGyUtSruh9w&bvm=bv.75097201,d.b2U

I was also interested in their conclusions about the contributions of the best & brightest versus raising the bar for all.  I had previously seen some research seeming to show that the best & brightest contribute the most to technological innovation and economic growth - http://www.sciencedirect.com/science/article/pii/S0160289614000476  But Hanushek et al's conclusions that we should focus both on the gifted and on not leaving anyone behind seems to be based on stronger evidence.

Forum Post for Saving Schools

** Based on the material presented in this section, what do you feel is the appropriate role that empirical evidence should play when making educational policy decisions? Do you believe policy makers primarily rely on empirical evidence?

Empirical evidence should play a huge role in policy decisions, assuming that the research has been done well, is reproducible, and has external validity showing that the results are likely to apply to the general population. Unfortunately as mentioned in the videos, it's often hard to get good research. Educational experiments on children may be unethical or just infeasible. Observational studies may have confounding factors that are actually responsible for the differences in results. Quasi-experiments don't always happen for the factors you're trying to study, or the results may not transfer to a more general set of students.

Also any policy changes need to made after looking at the whole research base, not just one or two studies. As we often see in medicine, one study will show that Vitamin X increases lifespan, and then a year later, another study shows that Vitamin X decreases lifespan. Perhaps more research needs to be done to figure out the actual effects of Vitamin X, or to see if it affects different people differently. But policy should not dictate that everyone gets huge doses of Vitamin X.

I think the policy makers are starting to rely more on empirical evidence. More groups are gathering research together in ways that non-researchers can better understand -
http://coalition4evidence.org/
I feel like the main issues are not so much with getting policy makers to recommend evidence-based practices, but rather with getting schools to implement evidence-based practices with fidelity. Scaling up programs that work is the hard part. And unfortunately when programs aren't scaled effectively, then the next set of research shows that the intervention doesn't work – e.g. Head Start.

Response to Other Student

Responding to another student's intro post...

Hi there ****,
I'd love to talk more about what you're working on, as I also used to own an educational center, am helping with a nonprofit, and am in the Math for Teaching program!  :-)  Feel free to email me at teresaeg@gmail to connect, if you want.

In response to your answers to the questions...
I definitely agree that teaching is not valued enough in US society.  Just paying them more would not immediately fix the problem, but I do think that's one step along the way, as it would hopefully start to attract a wider (and better?) pool of candidates.  As you mentioned, the lack of rigor and selectivity is a hugh issue.  Have you seen this?  http://www.joshuakennon.com/sat-scores-ranked-by-intended-college-major-show-teachers-are-below-average/  On average, teachers (or rather college students who intend to become teachers) don't even score at the mean for the SAT.  Yes, there are a lot of people who become teachers but had other majors besides education - but there's still a point to be made. 
If you haven't already, I'd recommend reading about Finland's teacher training - first of all, there's competition to get in. 
http://www.washingtonpost.com/blogs/answer-sheet/wp/2013/05/15/what-if-finlands-great-teachers-taught-in-u-s-schools-not-what-you-think/
http://www.ncee.org/programs-affiliates/center-on-international-education-benchmarking/top-performing-countries/finland-overview/finland-teacher-and-principal-quality/

On your second answer, I also agree with you that autodidacticism is critical.  There is so much information around us now - if students are able to learn on their own and seek out what they need, then they can learn so much faster.  Do you have any ideas on how to teach/foster independent learning?  Consistently offering opportunities and allowing students to pursue the topics that they're interested in seems to show some results - also starting early, as in start in preschool!  But often by high school, if they've been through so many years of teacher-directed learning, I find it hard to get all of the students to take a more self-directed approach.

Saturday, September 13, 2014

Find A Mission Statement

Initial 'assignment' for NonProfit Management - find a mission statement (or several) for a nonprofit to analyze in the next class.

I was just looking online for educational non-profits, and found this webpage with many organizations - and their mission statements!
https://www.myphilanthropedia.org/top-nonprofits/national/education/2014

I'm most interested in early education, so Jumpstart is one non-profit that I follow.  I actually couldn't find a specific mission statement on their current website, but based on a web search, it seems as if their (previous?) mission statement is...
"Jumpstart's mission is to ensure that all children in American enter school prepared to succeed. Year-round, Jumpstart recruits and trains thousands of college students and community volunteers to work with preschool children in low-income neighborhoods, helping them to develop the language, literacy, and social skills they need to succeed in school and in life."  In their blog posts, they mention a shorter mission of "to work toward the day every child in America enters school prepared to succeed"

I'm also interested in educational leadership, so I've started looking at New Leaders.  Their mission and vision are front and center on their webpage...
"Our mission is to ensure high academic achievement for all children, especially students in poverty and students of color, by developing transformational school leaders and advancing the policies and practices that allow great leaders to succeed.
VISION - We envision a day when there is educational excellence and equity in America – when our country’s public schools ensure that every student is prepared for success in college, careers and citizenship."

Intro for Scaling Up Excellence

Hi there everyone,

My name is Teresa Gonczy.  I just sold one business (local, not scaled), and am taking some time off to study.  I'm doing a masters in educational leadership, and am interested in how educational solutions can be scaled.  Previously, I helped to start a character elementary school and a family-friendly makerspace.

I would love to meet anyone else who is interested in education!  I'm more on the people side (actual schools/nonprofits that work with the children) and less on the edtech side.

In the last six months, who has taught you a valuable lesson about scaling up excellence?
In the last six months, several of my friends who founded start-ups stepped down/over from their original CEO positions into strategy or technology positions.  The lesson that I took from that is to let go and make sure that you're putting the right people in the right positions - which as you scale, may mean putting someone else in charge.

Classes for the Fall

* I'm going to be taking four graduate-level online courses through Harvard Extension this fall. (Unfortunately they won't let me take more!)

Math for Teaching Arithmetic - http://www.extension.harvard.edu/courses/13787
Quantitative Research Methodology - http://www.extension.harvard.edu/courses/14562
History, Politics, & Policy in US Education - http://www.extension.harvard.edu/courses/14604
Leading & Managing Non-Profit Organizations - http://www.extension.harvard.edu/courses/13357

* I'm also going to be taking a course through Harvard Kennedy School's Executive Education.


* And a course through UC Irvine's online programs.

* And a class through Stanford Continuing Studies.

Building Interpersonal Skills: An Experiential Workshop - https://continuingstudies.stanford.edu/courses/detail/20141_COM-19-B

* As well as a few MOOCs through Coursera, EdX, and NovoEd.  Some of them are repeating information from other courses I'm taking, but it's good to hear the info in different ways and from different perspectives.

Data Analysis and Statistical Inference - https://class.coursera.org/statistics-002
Intro to Financial Accounting - https://class.coursera.org/accounting-002
 
* Going forward, possible other classes I will be taking in the future...
Advanced Quantitative Research Methodology - http://www.extension.harvard.edu/courses/24261
Higher Education Management - http://www.extension.harvard.edu/courses/23211
Leadership, Organizing, and Action - https://exed.hks.harvard.edu/Programs/loa/overview.aspx
Intro to Operations Management - https://www.coursera.org/course/operations
Questionnaire Design for Surveys - https://www.coursera.org/course/questionnairedesign
Training & Learning Programs for Volunteers - https://www.coursera.org/course/commhealthworkers
Intro to Decision Quality - https://novoed.com/DQ101-4-2014






Wednesday, September 10, 2014

Intro for Educational Policy

My intro post on the forums for Harvard Extension - History, Politics, and Policy in US Education...

Hi there, I'm Teresa Gonczy, and I'm an entrepreneur and educator. I'm in Los Angeles right now, although I spent today putting a bunch of stuff in storage in order to start driving cross country in a few weeks to be based out of Chicago for the next year. Most recently, I owned an infant and family educational center here in LA. Previously, I helped to start a charter elementary school as well as a family-friendly makerspace. I also mentor teen entrepreneurs as part of the Thiel Fellowship, and help to organize the BIL Conference, a participant-powered unconference similar to TED. I sold my educational center a few months ago, and am taking some time right now to do a masters degree through Harvard Extension. I'm taking this course because I'm interested in how I can expand my influence in the educational world – to see what reforms have worked or not worked in what areas, and to connect with others who might be working in the field. Looking forward to talking more with you all over the course! :-)

1. What is the biggest problem facing the United States’ public school system? At this stage in the course, what do you think needs improvement / change?
I would say that the biggest problem for the public school system is educational equity. But remembering that equity is not the same thing as equality. Different students have different needs, whether they're special needs or gifted, low income or high income, predisposed to enjoy math or to enjoy literature, or just smack dab in the middle of everything. We need all students to be achieving at their own highest level of potential.
In order to move toward educational equity, a lot needs to improve and change. To help all students, we need to be able to differentiate instruction – which means that we need high quality teachers who are capable of coaching and leading students at different levels and with different interests – and we need those teachers in all classrooms, including low-income schools. To have high quality teachers, we need better preparation and development, ed schools and principals who really focus on instructional quality. Which also means that we need highly capable leadership, at the school level, at the district level, at the university level. The people are most important – although there are other initiatives that can also help with differentiating and delivering high quality learning to all students, such as technology, smaller class size or other rearranging of the typical classroom, socioemotional learning, building community, etc.


2. What are the most important goals of our school system, and why? (Economic growth, informed citizens, economic mobility, economic equality, etc.)
The most important goal of our school system is to help create the next generation that can push us forward as a society – technologically, socially, etc. We need people who are life-long learners because the world is changing so fast. People who can problem solve and think critically. Who can take and give feedback. Who are work well by themselves and with others. People who will be engaged with their work, their family, and their community. In order to move society forward, we need to help everyone to build their skills to function effectively, as well as cultivate the gifted who can make the ground-breaking leaps. If everyone is working at their highest level, economic growth and mobility will happen.

Friday, September 5, 2014

Initial Writing for Educational Policy

The YouTube video, 'Endangering Prosperity: A Global View of the American School,' provides a brief overview of the relative performance of U.S. students on international tests. Write a short response to the video describing the issues raised, the lessons you took away from the video, and how it fits (or doesn't) with your thinking on education politics and policy.

The teaser video for Endangering Prosperity takes a look at how kids in the United States rank 32nd on the worldwide PISA tests started in 2000. And even ten years after our initial poor showing in the PISA results, the US is still in the middle of the international pack. The video doesn't go into much specific detail about why we're 32nd or what might change our ranking, but it does point out that spending more money is not necessarily the answer. Other countries (and specific states within the US) get better results while spending less money. The video states that if we want to have a strong economy and be solving the big problems of the world, then we need some deep change in education – we've seen deep changes in how technology affects our home and work lives, but not yet in education.

The biggest lesson/reminder I took away from the video was about the money – while we certainly need some money to educate children, just throwing money at the issue won't help. We need to spend the money wisely on programs and systems that work. This is especially relevant to my interests in early childhood education, as universal preschool is gaining support currently. Federal and state governments are looking to spend many billions on early ed, yet while small high-quality preschool experiments have shown tremendous results, larger scaled-up programs often haven't shown significant results. What change needs to happen in the classroom, in the school, in the system, in order to produce the results that we know are possible? What insights can we take from other countries, as well as from within our country, about what works?

One issue that the video doesn't mention, but that I think about when looking at international comparisons... Are the higher-ranked countries smaller/less populous than the US? From a pure statistics perspective, the law of large numbers states that the larger the population, the more likely we'll be close to the mean. And from a scaling-up-programs perspective, it's easier to implement reforms with fewer students. We're dealing with a larger and more complicated issue than most countries.