So there's a story night things with friends coming up. Maybe I'll go, and if I do this will be the story that I tell:
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There's this little girl I know. She's about 9 or 10. She comes from a perfect little Christian family... or so people think. She knows that she's a little different from everybody else. She doesn't know how, but she knows that people treat her differently. Her teachers neglect her, her friends, if you can call them that, tease her, her dad abuses her, and her mom ignores her. Even her church friends bully and make fun of her. She thought church was supposed to be better. She was even raped there once. Of course she never told anybody. But everything else she told her dad, and he said, 'That's just what friends do to each other. Just go along with it and laugh.' But she never did laugh. It never felt right to laugh. She didn't know what to do or how to get help. Once she tried to ask her school teacher for help. As a class assignment, she wrote about what happened over the weekend at her house. She wrote about how her dad beat her mom and landed in jail overnight. But without even reading it, her teacher said that if she didn't want to share this to the class, she shouldn't write about it. So she erased everything and made up a silly story about being happy at a park. One day she just couldn't take anymore of this pain and hurt so she got a pencil and paper and started a letter to her friends.
'Dear Cathy and Rita,
I'm going to go away forever. Please don't come looking for me. I leave you with my favorite teddy bear and erasers.'
She took the paper, folded it, and put it in an envelope. She didn't know her friends' addresses, so she just wrote their names on the envelope and left it on her desk, where anyone could easily see it. Then she went to the kitchen and looked at the knives.
She didn't actually leave though. She felt like she didn't have enough courage.
She's much older now, and living happily. All the pain and suffering is gone, and she's living a wonderfully new life now. Just kidding. There's no such thing as happy ever after. That's just the face she puts on for others to see.
She's much older now, but she still bears all the scars of her childhood. They say that time heals all wounds. She's not so sure about that. Wounds leave scars, and she has a lot of those. Both emotional and physical. There are days when she can't help but relive those nightmares over and over. Some days are good. Some days are bad. But time might heal all wounds, you never know. So she waits.
Thursday, March 31, 2016
Wednesday, March 30, 2016
Math Curriculum Pt. 3
So I sent the final drafts in. The point of having the rough drafts published to this blog is so that just in case I don't get hired by Axiom Learning, my work and ideas are copyrighted so that Axiom can't profit off of my ideas without hiring me.
Tuesday, March 29, 2016
Math Curriculum Pt. 2
Writing a proposal less rough draft:
Background:
Through my many years of teaching students math, there is a consistent pattern that I always notice. Nearly all of my math students, regardless of their own confidence in their math abilities, claim to hate fractions. Fractions are a beautiful way to represent parts of a whole because of its accuracy, and shouldn't be a stumbling block. Many students that were doing excellently in math usually look for outside help when they reach the chapter of logarithms in Algebra 2 or PreCalculus. It's likely that they find the subject difficult because they learn about logarithms as a completely separate topic that is unrelated to other math topics. Moreover, I've noticed that Algebra itself tends to be a make or break for a lot of students when it comes to pursuing STEM classes later both in high school and college. Students will either make it through Algebra and go on Calculus and Physics, or they will find themselves despising the math and sciences, resolving to never touch the subject in college and go into Statistics to fulfill the math requirements of graduating high school.
The goal of this proposal is to give suggestions on how the math curriculum for grade schoolers can change so that they will not have to go through these hurdles during their math career and see STEM subjects in a different light.
Changes in the curriculum:
- Most of these change have to do with introducing notation early on.
1. Introducing parentheses in Kindergarten.
Kindergartners are learning how to count and add simple numbers with their fingers. Introducing parentheses at this age to addition isn't much of a stretch and it doesn't make the math that they are doing much more complicated. Why wait another 5 years to introduce parentheses only associated with PEMDAS?
Example: 2 + 5 + 3 = ? The answer is ten. What happens when we add parentheses here: (2 + 5) + 3 = ? We add the 2 and 5 first. So it become 7 + 3 = 10. What about 2 + (5 + 3) = ? Now we add the 5 + 3 first. So it becomes 2 + 8 = 10.
An addition worksheet that the students would do would include many problems with the exact same numbers with parentheses moved around. With practice and repetition, students will come to know the purpose of parentheses and how they affect addition. We can extend this to subtraction, multiplication, and division.
2. Introducing parentheses and the dot symbol as other symbols that represent multiplication
We teach students multiplication using the 'x' symbol. Students are so used to using the 'x' to represent multiplication, but abruptly stop using it when starting Algebra. Algebra has so many notation changes that students have a difficult time keeping track of what represents division and multiplication and the 'x' symbol as a variable. Instead, we can use the opportunity to show that there are multiple notations to represent the same thing.
Example: What is 2 x 3? What about 2(3)? (2)3? (2)(3)? 2.3? (Note: I will fix this in Microsoft Word).
A multiplication worksheet that the students would have with problems with similar numbers using the different style of notations so that they can get used to it.
3. Introducing the fraction notation as another form as division
I've noticed that students in the 10th and 11th grade are still confused when it comes to fractions. They have not yet associated fractions with divisions, and that association is not explicitly taught. Fractions tend to be in a completely different category than division. We can resolve this issue by having students make this association early on. Terms such as 'numerator' and 'denominator' are not important at this stage and can be learned later on.
Just like how I propose to teach multiplication using the multiple types of notation, I propose to teach division by including the fraction notation.
Background:
Through my many years of teaching students math, there is a consistent pattern that I always notice. Nearly all of my math students, regardless of their own confidence in their math abilities, claim to hate fractions. Fractions are a beautiful way to represent parts of a whole because of its accuracy, and shouldn't be a stumbling block. Many students that were doing excellently in math usually look for outside help when they reach the chapter of logarithms in Algebra 2 or PreCalculus. It's likely that they find the subject difficult because they learn about logarithms as a completely separate topic that is unrelated to other math topics. Moreover, I've noticed that Algebra itself tends to be a make or break for a lot of students when it comes to pursuing STEM classes later both in high school and college. Students will either make it through Algebra and go on Calculus and Physics, or they will find themselves despising the math and sciences, resolving to never touch the subject in college and go into Statistics to fulfill the math requirements of graduating high school.
The goal of this proposal is to give suggestions on how the math curriculum for grade schoolers can change so that they will not have to go through these hurdles during their math career and see STEM subjects in a different light.
Changes in the curriculum:
- Most of these change have to do with introducing notation early on.
1. Introducing parentheses in Kindergarten.
Kindergartners are learning how to count and add simple numbers with their fingers. Introducing parentheses at this age to addition isn't much of a stretch and it doesn't make the math that they are doing much more complicated. Why wait another 5 years to introduce parentheses only associated with PEMDAS?
Example: 2 + 5 + 3 = ? The answer is ten. What happens when we add parentheses here: (2 + 5) + 3 = ? We add the 2 and 5 first. So it become 7 + 3 = 10. What about 2 + (5 + 3) = ? Now we add the 5 + 3 first. So it becomes 2 + 8 = 10.
An addition worksheet that the students would do would include many problems with the exact same numbers with parentheses moved around. With practice and repetition, students will come to know the purpose of parentheses and how they affect addition. We can extend this to subtraction, multiplication, and division.
2. Introducing parentheses and the dot symbol as other symbols that represent multiplication
We teach students multiplication using the 'x' symbol. Students are so used to using the 'x' to represent multiplication, but abruptly stop using it when starting Algebra. Algebra has so many notation changes that students have a difficult time keeping track of what represents division and multiplication and the 'x' symbol as a variable. Instead, we can use the opportunity to show that there are multiple notations to represent the same thing.
Example: What is 2 x 3? What about 2(3)? (2)3? (2)(3)? 2.3? (Note: I will fix this in Microsoft Word).
A multiplication worksheet that the students would have with problems with similar numbers using the different style of notations so that they can get used to it.
3. Introducing the fraction notation as another form as division
I've noticed that students in the 10th and 11th grade are still confused when it comes to fractions. They have not yet associated fractions with divisions, and that association is not explicitly taught. Fractions tend to be in a completely different category than division. We can resolve this issue by having students make this association early on. Terms such as 'numerator' and 'denominator' are not important at this stage and can be learned later on.
Just like how I propose to teach multiplication using the multiple types of notation, I propose to teach division by including the fraction notation.
4. Introduce Logarithms after introducing roots (square, cube, etc.)
Students learn about exponents and their properties in 5th and 6th grade. They also learn how to go backwards using square and cube roots. It's not a difficult jump for students to learn about logarithms at the same time.
Example: 4^2 = 16. Sqrt(16) = 4 Log4(16) = 2 (Note: Adjust using Word)
By introducing logarithms early, Students won't be as intimidated when they learn about more properties of logarithms later. Just as students are introduced to roots but learn more about their properties, graphs, etc, later, they can learn what logarithms are at the same time but learn more about their properties later on. There's no need to have a three or four year gap between learning about exponents and then learning about logarithms.
5. Incorporating Algebra into Grade School math
At least a year of math (Pre-Algebra and parts of Algebra 1) is dedicated to learning how to manipulate variables and solving algebraic equations that can be easily incorporated all throughout grade school math.
How to change the way students feel about math, particularly algebra? Start by integrating Algebra concepts very early on, with Algebra notation, so that the Algebra notation itself wouldn't be a shocker when they get to 5th or 6th grade. Kindergarten students know 2 + 3 = 5. That means __ + 3 = 5 and __ is 2. So x + 3 = 5 then x = 2. and show that 2 = 5 - 3. (Now I'm getting too much into detail and this should be in the content section) If kids are learning division and multiplication and fractions, have Algebra with fractions and multiplication and division.
Instead of having the answer to a word problem be the main focus of the lessons, possible writing them in algebraic notation be a main focus and solving be more of an afterthought. Because word problems also tend to be a bane of a student's existence. Basically the idea is don't suddenly teach Algebra as a fresh topic in 6th grade, but rather have all of 6th grade Algebra 1 be integrated throughout the 1st through 5th grade material.
Math Curriculum
Writing a proposal very rough draft:
Format:
Background (why I'm writing this proposal)
Introduction (what I'm planning on doing/changing)
Content (I, II, and III)
Summary
Background:
I have been teaching the maths and sciences for nearly ten years. I've taught in small classes, large classes, and individual one-on-one stufff..... I've also taught students of all ages, but there are certain things that I've noticed a trend in... Nearly all of my math students claim to hate fractions. Even those good at math tend to prefer decimals over fractions. There's no reason to hate fractions because they make things very accurate, but even good math students hate them. Maybe it's because they never learned it correctly or something... I've also noticed that many students that start to need outside help in math start in Algebra 2 or PreCalc when they start learning about logarithms. Logarithms isn't very hard to learn. It's just the opposite of an exponential, like taking a square root is the opposite of a square. But I understand why they find the subject difficult. It's because they're first introduced to the concept in high school and taught like it's a completely separate thing. And lastly, I also noticed that Algebra class in high school is the make or break for a lot of students when it comes to learning more STEM-approached stuff later in life. They'll either make it through Algebra
----
Challenge of the month
Jake is looking at Anna. Anna is looking at George. Jake is married. George is not married. Is a married person looking at a not-married person? Yes, no, or can't tell?
Answer is yes. Doesn't matter if Anna is married or not. If she's not married, then Jake is looking at Anna so yes. If she is married, then she's looking at George so yes.
----
... so they'll either make it through Algebra fine and go on to Calculus and study science-y related things in college, or they'll completely despise math and go into Statistics to fulfill the math requirements of graduating and will resolve that they will never touch the subject again in college. The goal of this proposal is to teach math in such a way while the students are in grade school that they will not have to go through these hurdles during their math career and will see STEM subjects in a different light. Basically they won't be scared shitless of math and science.
Introduction:
How to teach fractions in a way that is less scary? Well first introduce the fraction notation when kids are learning division. One of the biggest issues that I see is that kids, even when they're in 10th or 11th grade aren't able to understand that division is the same is fractions. They see fractions, and in their mind fractions are in a completely different category. Resolve this issue by having students associate fractions with division early on. Knowing the terminology such as 'numerator' and 'denominator' are not important at this stage, and can come later on.
How to teach logarithms that won't have kids hating their class? Teach logarithms when teaching square roots and cube roots. They know what exponents are in 5th or 6th grade, and they know what square roots and cube roots are by 6th and 7th grade. Why wait another three or four years before teaching about logarithms? There's no real difference between logarithms and roots, so just teach them simple logs along with roots. Of course, students learn about more properties or roots as they mature in math, and so they can learn more about logs later as well, but introduce the subject early on, so the topic isn't scary.
How to change the way students feel about math, particularly algebra? Start by integrating Algebra concepts very early on, with Algebra notation, so that the Algebra notation itself wouldn't be a shocker when they get to 5th or 6th grade. Kindergarten students know 2 + 3 = 5. That means __ + 3 = 5 and __ is 2. So x + 3 = 5 then x = 2. and show that 2 = 5 - 3. (Now I'm getting too much into detail and this should be in the content section). Instead of having the answer to a word problem be the main focus of the lessons, possible writing them in algebraic notation be a main focus and solving be more of an afterthought. Because word problems also tend to be a bane of a student's existence. If kids are learning division and multiplication and fractions, have Algebra with fractions and multiplication and division. Basically the idea is don't suddenly teach Algebra as a fresh topic in 6th grade, but rather have all of 6th grade Algebra 1 be integrated throughout the 1st through 5th grade material.
Other random shit:
Why keep the multiplication as the 'x'? Ex: 2x3 = 6. But what about 2(3)? This is lost on so many student entering Algebra, although it shouldn't be. It's the notation. Notation itself is such a source of confusion, why can't we introduce the notation early on? If we give the students the association between the multiple notations there wouldn't be any confusion. So a math worksheet with lots of multiplication for 1st graders could look like a combination of multiple notations with problems that are more or less exactly the same. Same thing with division... Use division symbol and fraction symbol as different notations of the same thing. Introduce parenthesis in kindergarten even!! They can add multiple numbers already by counting on their fingers. 3 + 5 + 2 = 10!! But what happens when you do 3 + (5 + 2) =? Well we do parenthesis first! It's not a difficult introduction. It doesn't even make anything more complicated. Kids can understand these things. But why wait for 5 more years before parentheses are introduced?
Format:
Background (why I'm writing this proposal)
Introduction (what I'm planning on doing/changing)
Content (I, II, and III)
Summary
Background:
I have been teaching the maths and sciences for nearly ten years. I've taught in small classes, large classes, and individual one-on-one stufff..... I've also taught students of all ages, but there are certain things that I've noticed a trend in... Nearly all of my math students claim to hate fractions. Even those good at math tend to prefer decimals over fractions. There's no reason to hate fractions because they make things very accurate, but even good math students hate them. Maybe it's because they never learned it correctly or something... I've also noticed that many students that start to need outside help in math start in Algebra 2 or PreCalc when they start learning about logarithms. Logarithms isn't very hard to learn. It's just the opposite of an exponential, like taking a square root is the opposite of a square. But I understand why they find the subject difficult. It's because they're first introduced to the concept in high school and taught like it's a completely separate thing. And lastly, I also noticed that Algebra class in high school is the make or break for a lot of students when it comes to learning more STEM-approached stuff later in life. They'll either make it through Algebra
----
Challenge of the month
Jake is looking at Anna. Anna is looking at George. Jake is married. George is not married. Is a married person looking at a not-married person? Yes, no, or can't tell?
Answer is yes. Doesn't matter if Anna is married or not. If she's not married, then Jake is looking at Anna so yes. If she is married, then she's looking at George so yes.
----
... so they'll either make it through Algebra fine and go on to Calculus and study science-y related things in college, or they'll completely despise math and go into Statistics to fulfill the math requirements of graduating and will resolve that they will never touch the subject again in college. The goal of this proposal is to teach math in such a way while the students are in grade school that they will not have to go through these hurdles during their math career and will see STEM subjects in a different light. Basically they won't be scared shitless of math and science.
Introduction:
How to teach fractions in a way that is less scary? Well first introduce the fraction notation when kids are learning division. One of the biggest issues that I see is that kids, even when they're in 10th or 11th grade aren't able to understand that division is the same is fractions. They see fractions, and in their mind fractions are in a completely different category. Resolve this issue by having students associate fractions with division early on. Knowing the terminology such as 'numerator' and 'denominator' are not important at this stage, and can come later on.
How to teach logarithms that won't have kids hating their class? Teach logarithms when teaching square roots and cube roots. They know what exponents are in 5th or 6th grade, and they know what square roots and cube roots are by 6th and 7th grade. Why wait another three or four years before teaching about logarithms? There's no real difference between logarithms and roots, so just teach them simple logs along with roots. Of course, students learn about more properties or roots as they mature in math, and so they can learn more about logs later as well, but introduce the subject early on, so the topic isn't scary.
How to change the way students feel about math, particularly algebra? Start by integrating Algebra concepts very early on, with Algebra notation, so that the Algebra notation itself wouldn't be a shocker when they get to 5th or 6th grade. Kindergarten students know 2 + 3 = 5. That means __ + 3 = 5 and __ is 2. So x + 3 = 5 then x = 2. and show that 2 = 5 - 3. (Now I'm getting too much into detail and this should be in the content section). Instead of having the answer to a word problem be the main focus of the lessons, possible writing them in algebraic notation be a main focus and solving be more of an afterthought. Because word problems also tend to be a bane of a student's existence. If kids are learning division and multiplication and fractions, have Algebra with fractions and multiplication and division. Basically the idea is don't suddenly teach Algebra as a fresh topic in 6th grade, but rather have all of 6th grade Algebra 1 be integrated throughout the 1st through 5th grade material.
Other random shit:
Why keep the multiplication as the 'x'? Ex: 2x3 = 6. But what about 2(3)? This is lost on so many student entering Algebra, although it shouldn't be. It's the notation. Notation itself is such a source of confusion, why can't we introduce the notation early on? If we give the students the association between the multiple notations there wouldn't be any confusion. So a math worksheet with lots of multiplication for 1st graders could look like a combination of multiple notations with problems that are more or less exactly the same. Same thing with division... Use division symbol and fraction symbol as different notations of the same thing. Introduce parenthesis in kindergarten even!! They can add multiple numbers already by counting on their fingers. 3 + 5 + 2 = 10!! But what happens when you do 3 + (5 + 2) =? Well we do parenthesis first! It's not a difficult introduction. It doesn't even make anything more complicated. Kids can understand these things. But why wait for 5 more years before parentheses are introduced?
Monday, March 28, 2016
AJ Tutoring
Starting September, I'm going to be tutoring for AJ Tutoring in Menlo Park. I've already started attending their meetings and whatnot.
------
.... is what I had written over a year and a half ago. I started working for them, and then I got busy really quickly. Busy with moving, busy with work, busy with life... very busy. I had started these blogs to keep up on my life and also to spend the time. I had so many things to say about how amazing my life was, but was too busy to write anything down. So here's a big blurb on how I've been doing in the past year and a half.
-------
When I first started with AJ, everything seemed great. I was moving on with my life. I moved to a new apartment, I got a new job, something really fun that didn't feel like work, and I felt as if this was the next step to my life. Which was true. I really did like everything that was going on.
There were two things that seemed great at first but wasn't so great later: I had moved so far away that I left my old church and had to find a new one. Also the apartment... was terrible. I never want to live there again. Ever. It was awful. When we first moved in, everything seemed clean and neat. Apparently they hire a cleaning crew once a year during the moving season to make the apartment look great which only lasted a couple weeks. Every time it rained, the sewage would overflow, and it would leak directly into our bathroom and kitchen, and the hallways outside. Then there was the problem of cockroaches. The ENTIRE apartment complex had a huge cockroach infestation. It was disgusting. Unfortunately by the time we noticed that the apartment complex was a terrible place to live, we were several months into our lease and we couldn't break it.
I also had a very difficult time finding a good church. I feel like a good church has to have a lot of things going for it. It needs to have a good pastor, good members, and good fellowship. Good here is quite arbitrary. When I think 'good,' I think of someone that has a decent sense of morals that match up with mine, godly, friendly, warm, inviting, and especially caring for others around them. I hadn't been able to find a good church until just several weeks ago. So the past year and a half was
---------
And that part that I had written above was two weeks ago. Which means that I had time to hang out with the people at the church and get to know them better... not really.
I tutor a lot on Sundays, Sundays are usually the most requested day of the week. I have to make sure not to schedule anyone during the afternoon during service so I can go but then I need to go to tutoring right after. But that's not that bad, I like having an excuse to leave. I'm not very comfortable in group settings. But there are also a lot of new people. Apparently I wasn't the only new person to join. There were probably about 5 or 6 other newcomers, and when a quarter of the entire group are people who are new, it's hard to get a friendly conversation going. Especially if I don't know who I'm talking to. Then there's the case of lunch. The church stopped serving lunch for this year. Just snack foods and donuts. So if I want some real food before I go back to work, I have to leave early. Then there's Bible study. The church used to have Bible studies every week, alternating between Thursdays and Fridays so that everyone could get a chance to go. But for some reason, now that there's a huge influx of new people, they thought that reducing the number of Bible studies to every other week would be a great idea. And only on Thursdays. Which means that I can't go because Fridays are my only day off. Then the last two weeks, they have a church-wide vote on who would be elected for certain positions in the church, which meant that right after the worship service, the people who have been members of the church for a while would stay behind for an hour in the sanctuary to vote while everyone else would leave. So basically the entire past month I've started attending this church I haven't had much of an opportunity to get to know anyone.
-------
It's been a couple months since then. I'm going to stop this post and maybe (but most likely not) come back to this. On to new things.
------
.... is what I had written over a year and a half ago. I started working for them, and then I got busy really quickly. Busy with moving, busy with work, busy with life... very busy. I had started these blogs to keep up on my life and also to spend the time. I had so many things to say about how amazing my life was, but was too busy to write anything down. So here's a big blurb on how I've been doing in the past year and a half.
-------
When I first started with AJ, everything seemed great. I was moving on with my life. I moved to a new apartment, I got a new job, something really fun that didn't feel like work, and I felt as if this was the next step to my life. Which was true. I really did like everything that was going on.
There were two things that seemed great at first but wasn't so great later: I had moved so far away that I left my old church and had to find a new one. Also the apartment... was terrible. I never want to live there again. Ever. It was awful. When we first moved in, everything seemed clean and neat. Apparently they hire a cleaning crew once a year during the moving season to make the apartment look great which only lasted a couple weeks. Every time it rained, the sewage would overflow, and it would leak directly into our bathroom and kitchen, and the hallways outside. Then there was the problem of cockroaches. The ENTIRE apartment complex had a huge cockroach infestation. It was disgusting. Unfortunately by the time we noticed that the apartment complex was a terrible place to live, we were several months into our lease and we couldn't break it.
I also had a very difficult time finding a good church. I feel like a good church has to have a lot of things going for it. It needs to have a good pastor, good members, and good fellowship. Good here is quite arbitrary. When I think 'good,' I think of someone that has a decent sense of morals that match up with mine, godly, friendly, warm, inviting, and especially caring for others around them. I hadn't been able to find a good church until just several weeks ago. So the past year and a half was
---------
And that part that I had written above was two weeks ago. Which means that I had time to hang out with the people at the church and get to know them better... not really.
I tutor a lot on Sundays, Sundays are usually the most requested day of the week. I have to make sure not to schedule anyone during the afternoon during service so I can go but then I need to go to tutoring right after. But that's not that bad, I like having an excuse to leave. I'm not very comfortable in group settings. But there are also a lot of new people. Apparently I wasn't the only new person to join. There were probably about 5 or 6 other newcomers, and when a quarter of the entire group are people who are new, it's hard to get a friendly conversation going. Especially if I don't know who I'm talking to. Then there's the case of lunch. The church stopped serving lunch for this year. Just snack foods and donuts. So if I want some real food before I go back to work, I have to leave early. Then there's Bible study. The church used to have Bible studies every week, alternating between Thursdays and Fridays so that everyone could get a chance to go. But for some reason, now that there's a huge influx of new people, they thought that reducing the number of Bible studies to every other week would be a great idea. And only on Thursdays. Which means that I can't go because Fridays are my only day off. Then the last two weeks, they have a church-wide vote on who would be elected for certain positions in the church, which meant that right after the worship service, the people who have been members of the church for a while would stay behind for an hour in the sanctuary to vote while everyone else would leave. So basically the entire past month I've started attending this church I haven't had much of an opportunity to get to know anyone.
-------
It's been a couple months since then. I'm going to stop this post and maybe (but most likely not) come back to this. On to new things.
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