Reflections/ Meg Strnat

“Spatial thinking is not an add-on to an already crowded school curriculum, but rather a missing link across that curriculum. Integration and infusion of spatial thinking can help to achieve existing curricular objectives.”

National Research Council, 2006, p. 7

“What’s the most exciting way we can study this?” Mr. Lauricella to his studens; Cultivating Curiosity in K-12 Classrooms

All Lessons

Avoid turning lessons into worksheet or packets.

Rearrange lessons to follow

. We remember:

20% of what we read30% of what we hear40% of what we see50% of what we say60% of what we do90 of what we see, hear, say, and do.

Keep an ongoing vocabulary wall chart where students can modify definitions Don’t overlook the Extension activities. Vary how structure lessons using SIOP activities.

Ongoing mental transformation. o “An emerging body of research suggests that when it comes to mathematics learning and achievement,

visual-spatial working memory plays a critical role. As educators, we need to be aware that students process and remember information through both verbal and visual-spatial modalities; whether we are teaching literacy or mathematics, we need to honour both modes of thinking and learning.” Mental transformation using composition and decomposition.

o Notice great questions in Try This! (Try This! all from http://www.edu.gov.on.ca/eng/literacynumeracy/LNSPayingAttention.pdf; paper is called “Paying Attention to Spatial Reasoning – Support Document for Paying Attention Mathematics Education K-12”

Designing: multiple views

http://www.edu.gov.on.ca/eng/literacynumeracy/LNSPayingAttention.pdf

Used in CRE Family Engineering Night

Constant reference to number line: o Balanced Math.

o Tip: When introducing children to the number line, remember that many children are not accustomed to thinking about numbers as entities that occupy space (i.e., as intervals or units). As a result, many children see number line activities as practice in counting on, paying attention to ordinality but not the spatial relationships between numbers. Watch for students who determine their own intervals or units without acknowledging the end points. http://www.edu.gov.on.ca/eng/literacynumeracy/LNSPayingAttention.pdf.

o Human number lines.

Ongoing use of graphs. Balanced Math: Inspecting Equations.o What mathematical thinking do you see? o Tie to curriculum.

http://www.edu.gov.on.ca/eng/literacynumeracy/LNSPayingAttention.pdf.

Lesson 1

*Instead of the preassessment in this lesson, ask students to respond in their math journals to: Explain how spatial reasoning is evident in geometry using specific geometry vocabulary.*At the end of this unit, ask students to respond in their math journals to: Explain how spatial reasoning is evident in geometry using vocabulary learned in this unit.

Lesson 2

*Explore the impact of the layout of a game board. Quote on board: Chess Masters “see” the arrangements of chess pieces in larger and

more meaningful chunks and are faster at recognizing different board patterns.” Source: http://www.nap.edu/read/11019/chapter/6#96. Small groups/share: How does this quote relate to spatial thinking?

Play Scrabble. Background: Mosher Butts, who invented the game in 1938 as Criss-Cross Words,

spent a great deal of time analyzing text samples during the development of the tile set. Attempting to pinpoint how common each of the 26 letters in the alphabet is in the English language, Butts manually tracked through the distribution of individual letters in text from sources like the New York Times. Based on his letter-frequency assessment, Butts established the breakdown of letters included in the set of 100 tiles and developed the corresponding point value distribution used in both Scrabble® and an earlier version of the game, Lexiko, both of which used the same point-based tile sets.”

http://www.amstat.org/publications/jse/v16n1/jernigan.html).

Small Groups/share: How would you justify changing the distribution of word tiles in a Scrabble game?

Small group/share Compare and contrast the Scrabble and Words with Friend game boards on butcher paper. Make sure you use geometry vocabulary.

Which game board would you prefer and why? (Game board sources: http://worldofstuart.excellentcontent.com/unlocked/scrabble/ukboard.jpg and http://www.wordplays.com/words-with-friends-cheat).

*How would you design a 3 dimensional Tic-Tac-Toe (or game of choice) game? Create your own game board design and rules. Justify the layout of your game by testing several designs. Write and test instructions.

*Create your own 3 dimensional games (this fits in with volume unit, too. Visit Caine’s Arcade and watch short film (http://cainesarcade.com/). Create your own 3 dimensional game. Research types of arcade games. Your game

can be like an arcade game or any type of game that is 3 dimensional. Justify the layout of your game by testing several designs. Write and test instructions.

Lesson 3

*Worksheet driven.

*Constant reference to number line: Tip: When introducing children to the number line, remember that many children are not accustomed to thinking about numbers as entities that occupy space (i.e., as intervals or units). As a result, many children see number line activities as practice in counting on, paying attention to ordinality but not the spatial relationships between numbers. Watch for students who determine their own intervals or units without acknowledging the end points.

*Coordinate planes Use handout on p. 32 to play Battleship to work on spatial reasoning and order pairs.

Make sure students keep track of ordered pairs called by both teams (Source: and https://s-media-cache-ak0.pinimg.com/236x/dd/53/df/dd53dfa42007a4396bf9d52320700bad.jpg.) More advanced students can use the more complicated 4-quadrant grid.