Introduction
The first big idea the book talks about is being comprehensive. It states that the big ideas are aligned with the content of the Common Core State Standards and reflects the emphasis defined by the National Council of Teachers of Mathematics’ Curriculum Focal Points.
The second big idea is being thoughtful about content. It discusses that they have clustered 26 big ideas into nine topics with a chapter devoted to each one. This choice reflects the sense of what an early childhood classroom should emphasize.
The third big idea is developmentally organized. This section discusses that a big idea is presented in an order that makes clear how later ideas can be built upon and refers to the ones presented earlier.
The last big idea is flexibility. This idea is used to complement the current math teaching we are doing. It is meant to enrich our understanding and allow a more powerful implementation of the curriculum. The understanding of the set of ideas should be helpful in different aspects throughout the school day.
Briefly describe the five strategic teaching practices on page 7.
The first strategic practice is mathematicizing the world around us. This section talks about how we have to “see” math around us and be alert to the way that math and mathematical problem situations are built into the children’s everyday lives.
The second strategic practice is making mathematics more than manipulatives. This section discusses that children need to be able to feel, touch, and move things around for them to be able to explore and make sense of their environment. Children need help to use them for mathematical purposes. The math just can’t be “hands-on” because math is abstract. Math needs to be represented in multiple ways as children must make connections between concrete experiences, symbols, pictures, and language.
The third strategic practice is recognizing receptive understanding. This section talks about how teachers need to be aware of nonverbal indications of what a child is thinking, including gestures and actions. Children’s language development benefits greatly from positive feedback that acknowledges, reinforces, or offers clarification of what the child is attempting to communicate. Many children arrive in early childhood classrooms with their home language being something other than English. These children are encouraged to talk about mathematical ideas in their home language. Teachers who make an effort to look for and recognize evidence of receptive understanding of mathematical ideas have an advantage with English Language Learners and all young children.
The fourth strategic practice is getting mathematics into children’s eyes, ears, hands, and feet. This section talks about multimodal learning which refers to a learning situation that engages multiple sensory and action systems of the learner. Singing, jumping, dancing, and storytelling offer opportunities for multimodal learning. Auditory inputs such as singing a counting song to help children learn the number word sequence, while kinesthetic activities might include marching to a drumbeat to get a fee for one-to-one correspondences. When new ideas are presented in different ways, learners’ brains form more connections between those new ideas and other things they were already familiar with.
The fifth strategic practice is scaffolding children to construct their understanding. This section talks about how children are curious and competent problem solvers who can solve mathematically based problems that abound in their daily lives. It is important to nurture their inborn instinct to question and problem-solve. Good conversations give children opportunities to create and test theories. This is a powerful mechanism for the kind of learning that lasts and sustains new ideas. It ends by saying making your classroom a place where children enjoy sharing their ideas with us and their classmates can take time and patience but the math-learning payoff will be huge.
Chapter 1
Define the following terms and give an example for each: set, attributes, binary sort, people sort, multiple sets sort
Set: A set is any collection that is grouped together in some meaningful way
An example of a set is a group of toy race cars.
Attributes: Similarities such as color and shape
An example of an attribute would be the blue blocks in a set of blocks.
Binary Sort: Production of only two sets, one of which has a chosen attribute and one of which does not
An example of binary sort is having unmatched socks and putting all the green socks in a set and the other set would be socks that are not green.
People Sort: This is a game used to help children apply the knowledge of sorting. There will be circles placed on the ground and students have to categorize and sort themselves by shirt color, hair color, type of shoes, wearing glasses, etc. The point of the activity is not to understand the attributes but to develop the children’s familiarity with the sorting process and how it produces sets
An example of people sorting would be classmates sorting each other by each other's pants colors such as blue, black, white, etc.
Multiple Sets Sort: This type of sorting is different from binary sort because it is more than two sets that are produced and the attributes that define them are not opposites of one another such as (pink and not pink) but different types.
An example of multiple sets sort is sorting shapes by color and by the same shape.
What is an example activity for Binary Sort, Multiple Set Sort, and Comparing sets
An example of Binary sorting is a child sorting toys by ones that are blue and ones that are not blue.
An example of Multiple Set Sorting is a child sorting clothes by color and by season.
An example of Comparing sets is I would rather use paper straws than plastic ones.
Snapshot page 18- What was the teachable moment?
The teachable moment was that children have different viewpoints so the teacher had to be careful with how specific she set the categories. She made it clear to the students that the way she worded things could change the categories in which they were sorting themselves.
Chapter 2
Define the following terms and give an example for each: number sense, numerosity, nominal number, categorical number, cardinal numbers, ordinal numbers, subitizing, perceptual subitizing, conceptual subitizing
Number Sense: The ability to understand the quantity of a set and the name associated with that quantity
An example would be the number 1, one countermark, one finger held up, the number one on dice
Numerosity: quantity is an attribute of a set of objects and we use numbers to make specific quantities
An example would be money and how five, 20 dollar bills equal $100
Nominal Number: A numeral used for identification only
An example would be room number 124 for the science lab
Categorical Number: numbers that can be used in a set
An example would be the number six in a 6 side die
Cardinal Numbers: Provide the answer to the questions How many? And how much?
An example would be answer 3, when a student asks their teacher how many classmates are absent.
Ordinal Numbers: Refer to position in a sequence
An example would be a student saying they were first in line, then their other two classmates were second and third.
Subitizing: The ability to quickly perceive and name “how many” for collections of three, four, and five objects
An example would be recognizing the number of fingers someone is holding up
Perceptual Subitizing: The ability to identify if the number of items is three or less
An example would be holding up two toys and a young child identifying there are two toys
Conceptual Subitizing: Being able to identify numbers when the number of items gets a bit larger, as in four, five, or six
An example would be identifying the bigger numbers in a dice (4-6)
Search the internet for subitizing activities. Share 3 activities that reinforce this skill. Add the links to the activities to your Google Site.
-Using a ten frame
https://www.weareteachers.com/subitizing/
-Fly swatting game
https://www.weareteachers.com/subitizing/
-Watching a subitizing video
Search the internet for number sense activities. Share 3 activities that reinforce this skill. Add the links to the activities on your Google Site.
-Playdoh number mats
https://www.123homeschool4me.com/playdough-count-play-mats_8/
-Matching number cards to dominos
https://proudtobeprimary.com/building-number-sense-to-20/
-Associate numbers and numerals and make a cute poster
https://www.123homeschool4me.com/free-april-showers-number-sense_41/
Chapter 3
Define the following terms and give an example for each: rote counting, concrete experiences, rational counting, stable order principle, one-to-one correspondence, order irrelevance principle
Rote counting: Involves reciting the number names in order from memory
An example would be a child correctly counting to the number 10
Concrete Experiences: Counting has to be meaningful to young children in order to make sense
An example would be counting the meatballs going on a child's plate during lunchtime
Rational Counting: Involves matching each number name in order in a collection
An example would be a child saying one car, two cars, and three cars
Stable Order Principle: Counting words have to be said in the same order every time
An example would be counting to 1-5 (1,2,3,4,5)
One-to-one correspondence: One number is named for each object
An example would be a die with six up and six pretzels
Order Irrelevance Principle: No matter in what order the items in a collection are counted, the result is the same
An example would be scrabbling the ABC's up but there would still be 26 letters in the alphabet
What are the ways we can know a child has grasped the principle of cardinality? Some ways you can know if a child grasped the principle of cardinality is if they can label sets by quantity, without without counting. They can count out a given number, and they can count on or back from a given quantity.
What are your thoughts on the daily calendar time in the classroom? Beneficial or not? I think daily calendar time in the classroom is beneficial because it allows them to be exposed to the number order and how it works another aspect of their daily life.
Chapter 4
Define the following terms and give an example for each: counting all, counting on, part/whole relationships
Counting All: Is starting from 1 and continuing to account by 1 until they reach the total number for that round. It requires a concrete representation to operate upon.
Example-Some children in Ms. Green’s class counting each new chaser as they join the pursuit and they start at 1 until they finish however many were in the pursuit
Counting On: is counting on without needing to start at one. Usually counted on with smaller numbers often ones they can subitize.
Example- Tryce in Ms. Green’s class explained how there were already five people in the chase so the farmers are “six, seven, and eight” so there are eight in the chase now.
Part/Whole Relationships: When it is known that the parts of numbers and it is seen how they relate to other numbers, adding and subtracting with automaticity will be achieved. This involves a single collection or set
Example- Knowing the 3 and 4 are 7, so 7-3 must be 4.
What are the Big Ideas about Number Operations?
The first big idea is about many problem situations involving change. Such as adding to or taking away from a set. Those changes lend themselves to concrete models or to acting out as sets are joined or separated and then counted to find out How many more? It is also important for young children to make the more foundational generalization that adding increases and taking away decreases the quantity in a set. Sets can be changed by adding items (joining) or by taking some away (separating).
The second big idea is sets can be compared using the attribute of numerosity, and ordered by more than, less than, and equal to. This helps children build the understanding they need to think about a set in relationships to other sets and begin to make comparisons between numbers.
The third big idea is a quantity (whole) can be decomposed into equal or unequal parts; by the same token, the parts can be composed to form the whole. This understanding is a necessary foundation for operating on and with numbers. Children need to realize that smaller numbers are contained in larger numbers and be able to describe the parts of numbers. They need to be very comfortable with the idea that the quantity of five is not just a collection of ones but can be thought of instead as a group of three and a group of two.
What are factors that affect difficulty?
There are five factors that affect the level of difficulty in a problem situation.
The first one is that the size of the numbers make a big difference. Children are first able to use more advanced strategies such as counting on with smaller numbers. They will have a good understanding and can use their subitizing skills. When first constructing the relationships between numbers, it is especially important for children to have lots of experiences with smaller numbers. This provides a strong foundation as their number sense extends into higher numbers.
The second one is that the problem situations that we ask young children to model or “act out” have to be a fairly simple structure. It is important to keep reminding children of what the “unknown” is.
The third one is that many kindergarteners will need extensive guidance in solving situations that involve an unknown change such as (3+?=7) or an unknown start such as (?+4=7). Operations that don’t involve a change but call for composing and decomposing can also be challenging. Part/whole relationships between numbers within one set are more difficult to “act out” or directly model than a story in which an action changes the numbers of a set.
The fourth is that language issues make comparison situations difficult. Any comparison can be expressed in more than one way. It can be represented as 8 is more than 6 or 6 is less than 8. “How many more” is generally easier than “how many less or fewer”. Children seem to be more interested in statements about what is “more” and tend to find it uncomfortable to think of themselves as associated with what is “less”.
The fifth one is for any mathematical problem situation, knowing the story that lies behind the number operations helps young children make sense but can pose challenges for children whose first language is not english as well as for those who have language development issues. Children have to understand the story in order to use it mathematically. Giving children an opportunity to use felt-board figures or manipulatives to tell the story on their own and to model the problem situation provides opportunities for them to revisit and explore the situation again and again.
Chapter 5
Define the following terms and give an example for each: repeating patterns, temporal pattern, growing patterns, concentric patterns, movement patterns,
Repeating Patterns: These are named as so because they contain a segment that continuously repeat
Example-An example would be like Daniel’s train which was orange and always followed by blue. These patterns have a segment which is called unit of repeat. It can vary in length and level of complexity, but it is always the shortest string of elements that repeats. The unit of repeat can be thought about as the rule that governs a pattern.
Temporal Pattern: These are patterns that segment of signals that occur frequently and constantly.
Example-Some examples include the hours and minutes in time, the days of the week, weeks in a month, seasons, and even months in a year. These are constant and never end; they just repeat. Another example would be holidays because they occur on the same day in the same month, every year.
Growing Patterns:These are diverse repeating patterns which increase or decrease by a constant amount.
Example-An example would be the most basic growing pattern found in our counting system(1, 2, 3, 4…). Putting cubes together adding one by one until you get to the number 5 is another example.
Concentric Patterns: these patterns include circles or rings in which they grow from a common center.
Example-Some examples include ripples in still water when you throw a rock in the water. Or a hypnosis circle.
Movement Patterns: These are patterns that are made with movements within the body and can be made in a variety of ways. found in dance and walking
Example-An example would be following dance moves in a video. Or learning a dance from someone else. This pattern can be found in dance and walking like jumping or hopping in a certain beat.
Give 5 examples of how you can see patterns in a everyday classroom
The first example of how I can see patterns in an everyday classroom would be dancing to the same song or songs as a daily routine. They would use the same dance moves and the same song or songs which have the same lyrics and beat every time.
The second example would be making patterns with the toys, blocks, cubes, shapes. They can use the toys and put them in a certain order, blocks can be put together to make patterns such as height towers and compare them to others. Cubes can be put together to make different colored patterns such as AB, ABC, AABB, etc. Shapes can also be put together to make patterns.
The third example is having a class routine such as eating breakfast, doing morning work, going over the days of the week, months, etc, going to specials, lunch, nap time, and then time to go home. That would be an example that children get used to and know what is coming next in their daily schedule.
The fourth example would be storytelling such as nursery rhymes and the patterns that children recognize and can identify when asked what happens next in a story.
The fifth example would be making a people pattern by putting children in a stand and sit pattern and letting children figure out what comes next in the pattern.
Chapter 6
Define the following terms and give an example for each: capacity, unit, fair comparison
Capacity: This is the amount of a given substance that a container can hold without
Example-An example would be the amount of water a cup can hold before overflowing, the amount of weight a machine can hold before breaking, the amount of people that can be in a room before it becomes a hazard. Children can do activities to figure out that just because something looks like it can hold more than another or weigh more than something else it is not always the case. A long skinny tube that is 12 oz can also be held in a short wide cup that is also 12oz.
Unit:This is a crucial concept that is a nonobvious application of counting to the comparison of size attributes that makes it crucial. An individual component of a larger or more complex whole.
Example-Some examples would be inches, pounds and ounces, they are not things but ideas. Conventional units such as these subdivide a single size attribute in order to make it countable. Other units would be inches, feet, miles.
Fair Comparison: this is used to say that many attributes can be measured and be sized differently
Example-Measurements of uniforms, tuxes, formal wear, shoe sizes are all examples of these
Search the internet for activities that involve measurement for kindergarten students. Share 3 activities on your Google Site. Add the links to your resources.
A fun activity kids can use to measure is measuring their foot. They trace their feet with crayons, markers, or a pencil and get a ruler and see how many inches their feet are. They can compare the sizes with their classmates and make a chart of who has the same size feet as them. To take it a step further they can then connect cubes and see how many cubes are the same size as their feet.
https://www.weareteachers.com/teaching-measurement/
Another fun activity is connecting paper clips together to “measure” objects around the room. It would be an interactive activity and children can compare their different measurements they did. They will use the paperclip as “an inch” and write how many inches each object they measure is.
https://proudtobeprimary.com/measurement-activities/
The last activity is using string to wrap around different objects in the room and comparing the circumference to all different kids of objects in the room. They can even wrap it around their head, ankles, wrists, legs, and compare the sizes of their body parts to other body parts, for example, “my ankle is the same size as my wrist”.
https://www.splashlearn.com/blog/measurement-activities-for-kids/