Saturday, July 28, 2012
Math Expressions Video!
Here's a video we created from images & clips of Math Expressions over the past school year. Enjoy!
Math Expressions: From Fall, Winter, to Spring
Its been an amazing year working with the same 4th graders each week for the 2011-2012 school year. In fall, we used metaphors to understand the similarities between math and language. We then applied these skills in Winter by learning about Project Wildlife and organizing and executing a fundraiser for them. In Spring we finished the year by discussing the lobes of our brain and how they relate to problem solving.
Fall began by asking: "What is a number?" and ended with: "What is a variable?" We used analogs to language to help understand mathematics by comparing different kinds of numbers (negative/positive, whole/fraction, etc) to parts of speech(verb, noun, adjective) and comparing the order of operations to the order of a sentence or the organization of a letter.
The Winter fundraiser for Project Wildlife began by learning statistics about local wildlife and what Project Wildlife does as an organization. Students calculated how many volunteers they need on a daily basis and how many animals they help and then applied these data in making posters and signs. The students then raised money, determined how much they could raise if each student donated certain amounts, estimated the amounts they raised, and then decided what in-kind donations to spend the money on.
Each major lobe of the brain was covered in Spring and paired with a problem-solving strategy for math. The temporal lobe and reading the problem and picking out key terms, the temporal lobe and visualizing the problem, the parietal lobe and estimation, and the frontal lobe and checking ones answers. The year ended with a field trip to UCSD where students got a tour of the campus and an interactive brain-lab from the neuro-grad outreach group. (The quote of the day from students was - "I got to touch real brains.")
Photos, videos, and new games/activities in the other pages to come soon!
Fall began by asking: "What is a number?" and ended with: "What is a variable?" We used analogs to language to help understand mathematics by comparing different kinds of numbers (negative/positive, whole/fraction, etc) to parts of speech(verb, noun, adjective) and comparing the order of operations to the order of a sentence or the organization of a letter.
The Winter fundraiser for Project Wildlife began by learning statistics about local wildlife and what Project Wildlife does as an organization. Students calculated how many volunteers they need on a daily basis and how many animals they help and then applied these data in making posters and signs. The students then raised money, determined how much they could raise if each student donated certain amounts, estimated the amounts they raised, and then decided what in-kind donations to spend the money on.
Each major lobe of the brain was covered in Spring and paired with a problem-solving strategy for math. The temporal lobe and reading the problem and picking out key terms, the temporal lobe and visualizing the problem, the parietal lobe and estimation, and the frontal lobe and checking ones answers. The year ended with a field trip to UCSD where students got a tour of the campus and an interactive brain-lab from the neuro-grad outreach group. (The quote of the day from students was - "I got to touch real brains.")
Photos, videos, and new games/activities in the other pages to come soon!
Friday, September 9, 2011
Math Expression: Updates
So, of course its been far too long since we've last posted. I guess I'm not a natural blogger...
During spring quarter at UCSD, ISEE education collaborated with Linda Vista elementary school to offer an after-school program "Math Expressions" once a week. Although the program required more weeks than were left of school we "piloted" it anyway. We had many insights from our observations and interactions, and even deeper ones from our students.
A quick summary - all of which could use more detail:
- Address level of student's knowledge first (Ok this one is a no-brainer but without time to do so for the pilot program we got first hand experience on why its so important)
- Students themselves may not recognize that games and activities that use math ARE math. (e.g. multiplication tic-tac-toe which requires knowledge of multiplication to play is not understood as practicing math
- An hour a week is too short
Wednesday, April 6, 2011
CGI U
Hi all,
The ISEE education team recently participated in CGI U (Clinton Global Initiative University - http://www.cgiu.org/Default.asp) and was able to share their commitment to action to San Diego schools at the CGI U exchange. During this event we challenged CGI U attendees to one of my favorite activities - the magic cup of ice water.
To do this activity all you need is a cup, ice, water, and a permanent marker. Put the water and ice in the cup and mark the water level with the marker. Then make some predictions. What will happen to the water level when the ice melts? Will it rise? Fall? Or stay the same?
At CGI U 15% guessed above, 55% said below, and 30% same. After participants guessed, we asked them to explain their answers.
Those who said above argued that the ice would add more water to the cup upon melting because when the ice melted it would leave behind more water.
Those who said below argued that ice expands as a solid and therefore would leave behind less water when it melted.
Those who said the level will stay the same pointed to the d=m/v equations and many of them said they had done this experiment in a class before.
Who is right? Well we didn't tell anyone at the conference, instead they had to come here and let the question stew in their brain for a few days.
So now for the amazing solution check out the video below from youtube user onefivefour:
Not convinced? Here's another version (shorter) with a measuring cup:
So why does this happen? While its true that H2O is larger in its solid form than in its liquid form, when we think back to displacement and density equal to mass divided by volume, the solution becomes clear.
Lets say we have an ice cube mass m floating in water, in order to do so it must displace some of the water in the cup to hold itself up. This displacement is key because it pushes the water up slightly increasing the volume as apposed to a cup without any ice in it at all. When the ice melts, its density decreases and it fills the spaces it originally displaced, except this time with water so it smooths over.
Or if you're more of a number person...
density of water = 9x10^5 grams per cubic meter
density of ice = 1x10^6 grams per cubic meter
mass of water in cup = 1000 grams
mass of ice = 10 grams
v = m/d
vinitial = 10/9x10^5 + 1000/1x10^6
= 1 x 10^9 liters
vfinal = 1010/1x10^6
= 1 x 10^9 liters
Don't you just love it when math and science work?
Still don't believe us? Try it yourself! I've had students test this with once ice cubes, ten ice cubes, water level starting very low and water level starting at the brim of the cup. Just make sure to hypothesize, test, and understand.
Thanks to Bill Clinton, CGI U staff, UCSD staff, and all the wonderful attendees!
The ISEE education team recently participated in CGI U (Clinton Global Initiative University - http://www.cgiu.org/Default.asp) and was able to share their commitment to action to San Diego schools at the CGI U exchange. During this event we challenged CGI U attendees to one of my favorite activities - the magic cup of ice water.
To do this activity all you need is a cup, ice, water, and a permanent marker. Put the water and ice in the cup and mark the water level with the marker. Then make some predictions. What will happen to the water level when the ice melts? Will it rise? Fall? Or stay the same?
At CGI U 15% guessed above, 55% said below, and 30% same. After participants guessed, we asked them to explain their answers.
Those who said above argued that the ice would add more water to the cup upon melting because when the ice melted it would leave behind more water.
Those who said below argued that ice expands as a solid and therefore would leave behind less water when it melted.
Those who said the level will stay the same pointed to the d=m/v equations and many of them said they had done this experiment in a class before.
Who is right? Well we didn't tell anyone at the conference, instead they had to come here and let the question stew in their brain for a few days.
So now for the amazing solution check out the video below from youtube user onefivefour:
Not convinced? Here's another version (shorter) with a measuring cup:
So why does this happen? While its true that H2O is larger in its solid form than in its liquid form, when we think back to displacement and density equal to mass divided by volume, the solution becomes clear.
Lets say we have an ice cube mass m floating in water, in order to do so it must displace some of the water in the cup to hold itself up. This displacement is key because it pushes the water up slightly increasing the volume as apposed to a cup without any ice in it at all. When the ice melts, its density decreases and it fills the spaces it originally displaced, except this time with water so it smooths over.
Or if you're more of a number person...
density of water = 9x10^5 grams per cubic meter
density of ice = 1x10^6 grams per cubic meter
mass of water in cup = 1000 grams
mass of ice = 10 grams
v = m/d
vinitial = 10/9x10^5 + 1000/1x10^6
= 1 x 10^9 liters
vfinal = 1010/1x10^6
= 1 x 10^9 liters
Don't you just love it when math and science work?
Still don't believe us? Try it yourself! I've had students test this with once ice cubes, ten ice cubes, water level starting very low and water level starting at the brim of the cup. Just make sure to hypothesize, test, and understand.
Thanks to Bill Clinton, CGI U staff, UCSD staff, and all the wonderful attendees!
Friday, November 19, 2010
Beyond Vocab and Grammar
For English language learners and native speakers alike, learning new vocabulary and parts of speech can become difficult and tedious. Below are a few games I have been experimenting with recently to make learning English more comfortable, fun, and creative.
Write this, Draw that
Need: Paper, pencil, at least 3 players
How to play: Each player gets a piece of paper and has to write a sentence on it. Once they finish they fold the paper so that the sentence is covered and pass it to the player next to them. Upon receiving the piece of paper, the next player reads the sentence, folds the paper back, and then draws the sentence below. Next they pass the drawing and the next person looks at the drawing and writes a sentence about what is happening. They then fold the paper to cover the drawing but leave the sentence showing. Depending on the number of players, this can be repeated multiple times until the paper returns to its original writer. When this happens, read the original sentences out loud and show how they have been changed with drawings and rewritings.
Flash Act/Spell
Need: Playing board (can easily be made with circles or squares drawn on a piece of paper from start to finish with some squares colored in), dice or coin, items to represent players, vocab cards
How to play: First write down the vocabulary words on one side of a flash card (5 times for practice) and draw the word on the other side. Next have players put their pieces at the start of the playing board and use a coin flip (heads 1 space move, tails 2 space moves) or die to determine how the player moves. If the player lands on a normal space, they must guess the word from the drawing on the flashcard and spell it. If they land on a special space, the other player has to act out the word and it has to be guessed and spelled. Each time the word is guessed and spelled correctly the player gains one point. Whoever has the most points by the time they reach the finish wins.
Apples to Apples (SAT/Weekly Vocab Edition)
Need: Flashcards with vocab words
How to Play: Play just like the game Apples to Apples (http://www.letsplayapples.com/), but with your own cards that relate to vocabulary words. Either mix in with other words or things you like, or combine with an Apples to Apples deck.
MadLibs
Okay yes, MadLibs was mostly invented for family roadtrips but they can be really useful and entertaining when learning parts of speech. Not only do they allow an opportunity to remember what nouns, adverbs, etc, are but they also teach what these things do in a sentence and how they effect it.
Write this, Draw that
Need: Paper, pencil, at least 3 players
How to play: Each player gets a piece of paper and has to write a sentence on it. Once they finish they fold the paper so that the sentence is covered and pass it to the player next to them. Upon receiving the piece of paper, the next player reads the sentence, folds the paper back, and then draws the sentence below. Next they pass the drawing and the next person looks at the drawing and writes a sentence about what is happening. They then fold the paper to cover the drawing but leave the sentence showing. Depending on the number of players, this can be repeated multiple times until the paper returns to its original writer. When this happens, read the original sentences out loud and show how they have been changed with drawings and rewritings.
Flash Act/Spell
Need: Playing board (can easily be made with circles or squares drawn on a piece of paper from start to finish with some squares colored in), dice or coin, items to represent players, vocab cards
How to play: First write down the vocabulary words on one side of a flash card (5 times for practice) and draw the word on the other side. Next have players put their pieces at the start of the playing board and use a coin flip (heads 1 space move, tails 2 space moves) or die to determine how the player moves. If the player lands on a normal space, they must guess the word from the drawing on the flashcard and spell it. If they land on a special space, the other player has to act out the word and it has to be guessed and spelled. Each time the word is guessed and spelled correctly the player gains one point. Whoever has the most points by the time they reach the finish wins.
Apples to Apples (SAT/Weekly Vocab Edition)
Need: Flashcards with vocab words
How to Play: Play just like the game Apples to Apples (http://www.letsplayapples.com/), but with your own cards that relate to vocabulary words. Either mix in with other words or things you like, or combine with an Apples to Apples deck.
MadLibs
Okay yes, MadLibs was mostly invented for family roadtrips but they can be really useful and entertaining when learning parts of speech. Not only do they allow an opportunity to remember what nouns, adverbs, etc, are but they also teach what these things do in a sentence and how they effect it.
Multiplication Tic-Tac-Toe
Remember learning multiplication facts or times tables? Endless worksheets, memorization, and rewriting charts?
Well say goodbye to those beloved memories and get ready to try a fun game.
In multiplication tic-tac-toe, two players practice multiplication and forming strategies.
Here's how it works. The first player chooses two factors (the 1-9 on the game board) and places an item on each (paperclip, erasers, coins, etc). The player then crosses off or places their item on the product in the box above. Next, the second player moves one of the items on the factors to a different factor. For example, if the game begins with three and six selected, the next move can either move the three or six, but not both. The second player puts their mark on the product. Play continues until one player has marked four products in a row, column, or diagonal.
And yes, you can have two of the same factor selected at once.
I've tried this game several times so far and it has been a success. Not only is it helping me remember all that multiplication, but is a fun activity that students can take ownership of and discuss tactics and strategies of play.
Tuesday, October 26, 2010
Reading Activities
Reading is more than just sounding out letters. Its about finding the meaning, the purpose, and your own reaction to the sentences and stories that those letters create. In this more holistic view of what constitutes reading, activities that contain the high standards of comprehension and critical thinking are needed to deepen and assess these skills. Below is a list of such activities from materials from a lecture on reading in EDS 130 at UCSD.
After Reading Activities
Compare the story/text to a personal event
Poster Report
Mural
Compare/Contrast the characters in a Venn diagram.
Write a new ending for the story.
Write a report card for one of the characters.
Create a skit about the characters in the story.
Read a favorite passage into a recorder.
Play the part of a character and have someone interview you.
Write an advertisement of the book.
Make a TV scroll of a part of the story or historical event.
Write a letter recommending the book to a friend.
Write a diary entry from the point of view of the main character describing a main event in the story.
Make a timeline of events in the story, historical, or scientific event.
Prepare a newspaper article about the story.
Write a sequel to the story.
Give a book talk about what you read.
Write a cinquain or acrostic poem about the main character, historical figures, or events.
Create a puppet for one of the main characters.
Write a conversation between two characters.
Pretend you are a newspaper reporter writing a news article about a major event in the story.
Write a different ending to the story.
Create a book jacket for the story.
Research the author. Find out interesting facts to share with others who have read the book.
Make a diorama of a main event in the story.
Debates.
Choral speaking.
Retell a story or event using overheads/document camera.
Other Ideas:
Act out a scene from the story.
Choreograph a dance for a scene from the story or about what a character may have been feeling.
Create a comic about the story or an important part of the story.
Write a song from the point of view of the protagonist or antagonist.
Change the sex of the main character and discuss its effects on the story.
Another important aspect of reading is discussion questions, especially those with no clear answer. This challenges readers to construct hypotheses based on their observations of characters or situations in the text and prove them with evidence. Below are some open ended questions from the same lecture.
Did the author tell you enough?
What else would you like to know?
What did you find out that you didn't know before?
Tell me the main things that happened.
Were you able to guess what was going to happen?
Can you think of another way the story might have ended?
What do you remember most?
Why do you think the author wrote this?
Do you think there is a message in the book?What is it?
Do you like the illustrations? Why? Why not?
What do you think the illustrator needed to know in order to illustrate this story?
What puzzled you?
Have you ever read other books/stories/poems like this?Tell me about htem.
What character/part interested you most?
Is that character the most important person in the story? Why?
What characters didn't you like? Why?
Did any characters remind you of people you know? How so?
Did the characters change? In what way?
Has anything like this ever happened to you? Did you feel the same as the people in the story?
Have you read a story like this before? If so, was it different this time? What did you notice this time?
Were the events in this story realistic? Tell more.
How could these events really have happened? Explain
How did suspense/excitement get built up in this story?
What problems did the characters face? How did they solve them?
How/why is the life of this family similar/different from your own family life? Give some reasons.
Try to place yourself in this piece. Would you have reacted in the same way or would you do things differently? Why?
Its important to note what these questions are doing to the reader. Many of them ask the reader to relate the story back to their own lives as a sort of "litmus test" for creditability. Instead of simply studying at the story within its own context, these questions reach out to the reader's life to find truths as well as create relevance to the material. This technique is not only useful in reading and language classes, but in any course. When the material covered is brought back to the individual and their life the individual cane become motivated by the meaning derived from this interaction.
If you have any other reading activities or questions that should be on these lists please suggest them!
After Reading Activities
Compare the story/text to a personal event
Poster Report
Mural
Compare/Contrast the characters in a Venn diagram.
Write a new ending for the story.
Write a report card for one of the characters.
Create a skit about the characters in the story.
Read a favorite passage into a recorder.
Play the part of a character and have someone interview you.
Write an advertisement of the book.
Make a TV scroll of a part of the story or historical event.
Write a letter recommending the book to a friend.
Write a diary entry from the point of view of the main character describing a main event in the story.
Make a timeline of events in the story, historical, or scientific event.
Prepare a newspaper article about the story.
Write a sequel to the story.
Give a book talk about what you read.
Write a cinquain or acrostic poem about the main character, historical figures, or events.
Create a puppet for one of the main characters.
Write a conversation between two characters.
Pretend you are a newspaper reporter writing a news article about a major event in the story.
Write a different ending to the story.
Create a book jacket for the story.
Research the author. Find out interesting facts to share with others who have read the book.
Make a diorama of a main event in the story.
Debates.
Choral speaking.
Retell a story or event using overheads/document camera.
Other Ideas:
Act out a scene from the story.
Choreograph a dance for a scene from the story or about what a character may have been feeling.
Create a comic about the story or an important part of the story.
Write a song from the point of view of the protagonist or antagonist.
Change the sex of the main character and discuss its effects on the story.
Another important aspect of reading is discussion questions, especially those with no clear answer. This challenges readers to construct hypotheses based on their observations of characters or situations in the text and prove them with evidence. Below are some open ended questions from the same lecture.
Did the author tell you enough?
What else would you like to know?
What did you find out that you didn't know before?
Tell me the main things that happened.
Were you able to guess what was going to happen?
Can you think of another way the story might have ended?
What do you remember most?
Why do you think the author wrote this?
Do you think there is a message in the book?What is it?
Do you like the illustrations? Why? Why not?
What do you think the illustrator needed to know in order to illustrate this story?
What puzzled you?
Have you ever read other books/stories/poems like this?Tell me about htem.
What character/part interested you most?
Is that character the most important person in the story? Why?
What characters didn't you like? Why?
Did any characters remind you of people you know? How so?
Did the characters change? In what way?
Has anything like this ever happened to you? Did you feel the same as the people in the story?
Have you read a story like this before? If so, was it different this time? What did you notice this time?
Were the events in this story realistic? Tell more.
How could these events really have happened? Explain
How did suspense/excitement get built up in this story?
What problems did the characters face? How did they solve them?
How/why is the life of this family similar/different from your own family life? Give some reasons.
Try to place yourself in this piece. Would you have reacted in the same way or would you do things differently? Why?
Its important to note what these questions are doing to the reader. Many of them ask the reader to relate the story back to their own lives as a sort of "litmus test" for creditability. Instead of simply studying at the story within its own context, these questions reach out to the reader's life to find truths as well as create relevance to the material. This technique is not only useful in reading and language classes, but in any course. When the material covered is brought back to the individual and their life the individual cane become motivated by the meaning derived from this interaction.
If you have any other reading activities or questions that should be on these lists please suggest them!
Subscribe to:
Posts (Atom)