Briefly describe the Big Ideas
Some of the big ideas listed in the introduction. One of the big ideas is how mathematics concepts and skills can serve students as organizing structures for understanding in the very first years of elementary school and even in preschool. Numbers are used in any different ways. These include indicating amounts, specify position in sequencing, give names for a set, to act as shared reference points. The next big idea is building on young children's informational or everyday math knowledge, and it promotes the scientific understanding of basic math skills. counting can be used to find out how many of anything there is. Counting words should be said in order each time. The last number that is counted in a set is the product.
Briefly describe the five strategic teaching practices on page 7.
The five strategic strategies listed on page 7 goes into depth about many different ways that you can teach math and its concepts. The first strategy suggests that we should mathematize the world around us. This means that as instructors we should express how much math is used around us. We should be working to see the math around us in everyday lives and implement that into our teaching. When students come to realize how much math plays a part in our real life it becomes something that they want to learn more about. The second teaching strategy is to make mathematic more than the manipulatives. Children need concrete learning experiences. Meaning the that the younger they are, the more they need to move themselves around to explore new things in their environment. In a classroom it is normally filled with mathematical objects like unit blocks, but students must be helped to use these. The third strategy is recognizing receptive understanding. Teachers of the very young must be very aware of the nonverbal indications of what a child might be thinking. Mathematical language poses a great challenge for young learners because it focuses on abstractions. Especially the math words that compare attributes, for example heavier, shorter, longer, less, greater, equal to etc. There is a relationship being described with these concepts. The more abstract the idea the more complex it is for the student to learn. The fourth strategy is to get mathematics in children's eyes, ears, hands and feet. when singing jumping and dancing offers the opportunity for multimodal learning. When you do these types of activities with children, they are able to repeat these sounds, chants, songs or rhymes back to themselves. The fifth strategy is to scaffold children to construct their own understanding. Classroom teachers are able to make instructional decisions. When you walk into a classroom you will hear questions being asked like "how many is in there?" or "Which one has more?" These are mathematically based problem that will be used in everyday life. Worksheets and standardized measure are efficient and they look for right and wrong answers. However they bypass genuine understanding.
Chapter 1
Read the entire chapter. Highlight information that stands out to you.
Define the following terms and give an example for each: set, attributes, binary sort, people sort, multiple sets sort
set- is any collection that is grouped together in some meaningful way.
Attributes- can be used to sort collections into sets, they can be different colors and shapes that match items that are fully alike.
binary sort- can be described as a sorting algorithm that produces two sets. One set that has a chosen attribute and one that does not.
people sort- is a game that includes people and it goes by the attributes of the students. For example in the game they have a group stand in the hula hoop if they have curly hair and the group that does not stands in the other hula hoop.
multiple sets sort- includes more than two sets being produced, the attributes that are being compared are not the opposite of one another.
What is an example activity for Binary Sort, Multiple Set Sort, and Comparing sets
Binary sort can be described through this example. A student breaks a collection into two categories. She ignores the shape and only focuses on the color of pink that it is. She sorts the different shapes that can be separated into those that are pink and those that aren't. Over all binary sort can be described as a sorting algorithm that produces two sets. One set that has a chosen attribute and one that does not.
Multiple set sort-You can sort different shoes that focus on the attribute of laces Buckles or Velcro. Once the sets are created then they must be counted and sorted least from greatest. This aids in helping the student understand number sense and different attributes of objects that surround them everyday. Sorting things falls under algebra which encompasses the understanding of patterns and relationships.
Comparing sets- collections with varied attributes. For example students could spin a wheel with numbers. In three spaces they will dot however many the spinner lands on. Then they will compare the numbers within each box. Then color the box with the least dots red and the most dots green. The dots that are in between them will color yellow.
4.Snapshot page 18- What was the teachable moment?
The teachable moment was when Mrs. Simone had to be careful about what exactly she said to the students. She said that she can see that they are thinking hard. She suggested that they do it two different ways. She narrowed the four groups down to two that includes the no white and the some white. Then the students to have an understanding of how it changed from all white to not all white.
Chapter 2
Read the entire chapter. Highlight information that stands out to you.
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- is the ability to understand the quantity of a set and the name associated with the quantity.
numerosity- is a term that describes how many and is central to number sense development.
nominal number- a term that only refers to number when used in numeral identification. Does not indicate rank, quantity, or any other measurement.
categorical number-refers to number when used in numeral identification.
cardinal numbers- are numbers used to express the amount or quantity. These are counting numbers.
ordinal numbers- are used to the exact placement of a number. For example 1st, 2nd, or 3rd.
subitizing- refers to the ability of a student to instantly see how many dots are in a set.
perceptual subitizing- can occur when there is three or less items in a collection. This comes before conceptual subitizing because they must understand the smaller numbers first
conceptual subitizing- refers to helping children know just how many dots there might be with counting a dice or dominoes. The manipulatives that are used with subitizing are very important because it gives the student the ability to remember the quantity if these numbers.
Search the internet for subitizing activities. Share 3 activities that reinforce this skill. Add the links to the activities to your Google Site.
How to Use Subitizing Cards in the Classroom – Primary Delight (primarydelightteaching.com)
What is Subitizing? + FREE Activities - Mrs. Richardson's Class (mrsrichardsonsclass.com)
Subitizing Activities and Centers for Pre-K & Kindergarten (thekindergartenconnection.com)
Search the internet for number sense activities. Share 3 activities that reinforce this skill. Add the links to the activities on your Google Site.
Number Sense Activities for the Classroom - WeAreTeachers
Chapter 3
Read the entire chapter. Highlight the information that stands out to you.
Define the following terms and give an example for each:
rote counting- involves reciting the number names in order form memory. Ex. 1,2,3,4,5,6,7,8,9,10
concrete experiences- the counting has to be meaningful in order for children to fully understand the concept of counting. There are many different manipulatives that can be used to create concrete experienced. Physical objects should be used like toys, counting blocks, balls, or any type of toy.
rational counting- involves the matching of each number name in order to an object in a collection. This type of counting is a foundation or starting point for children who are in their early stages of learning numbers.
stable order principle- the sequence for how we count will never change and always stay the same. Ex. 1,2,3,4,5,6,7,8, etc.
one-to-one correspondence- means that one number in names for each object. This is a big skill or children to learn because they cannot fully grasp the concept right off the bat. This is hard for students to fully grasp because they are having to do the physical movement of their finger and the eye along objects, matching one number word to one object at a time until each object has been named a number.
order irrelevance principle- builds on the rule of stable order and further expands on and generalizes the idea behind one-to-one correspondences. The definition of order irrelevance principle is no matter in what order the items in a collection are counted, the results always stay the same. It does not matter if students count out of order, right from left, left from right, or from somewhere else. It matters if all the items are counted.
What are the ways we can know a child has grasped the principle of cardinality?
There are a few ways that we can tell if a student has grasped the concept of cardinality. One way to see is if you ask the child how many there are all together in the group. The child would name the last number that was counted and doesmt need to count again. The next way to identify if the child understands is to as the child to count a specific amount of items and create a set of given quantity. Another way is when given more items to take away or add, the child has the ability to count forwards or backwards instead of counting them all. Finally the last way to know if the child understands cardinality is by seeing if the child knows that the quantity will stay the same even around the fact that the place of the objects are able to change. Children normally will first learn to count before they understand “how many” objects they are actually counting in sets.
What are your thoughts on the daily calendar time in the classroom? Beneficial or no?
I think that the Calander routines that are used in classrooms are not beneficial besides enabling children to be educated on the months and days of the year. I don't believe that it is conductive or beneficial because it does not exercise the counting skills or number sense since the days are never in the same order. It is hard for us to grasps the understanding at a young age of the calendar because people find it challenging to count by sevens. However, I do believe that it does help students gain the understanding about how the days of the year are sequences as well as the days of the week. However, I do not think that they can gain an entire understanding of how the calendar work because these kids don't even understand time to the full extent. Therefore, some students might not even pay attention and this time is valuable and could be spent in other instruction with math subjects.
Watch this: https://www.youtube.com/watch?v=AODVbI2gG4Q
Chapter 4
Read the entire chapter. Highlight the information that stands out to you.
Define the following terms and give an example for each: counting all, counting on, part/whole relationships
counting all-is the first direct strategy that young children use to solve changing stories. This can involve the student increasing and decreasing until they reach the total number for that lesson. It requires a concrete representation to "operate" upon. There are many concrete ways that it can be represented, like cubes, fingers, or marks on paper.
counting on-is an effective counting strategy. As the teacher counts and says the words aloud the student holds up his fingers to show how many there are while she counts. The student normally starts out "counting all" with smaller numbers. There is also double count which is adding an amount to a number. For example six is one more than 5; seven is 2 more than 5; eight is 3 more than 5. This counting strategy is a bit more complicated than counting all.
part/whole relationships-involves a single collection or set. There is an unknown number that has to be figured out in the relationship to the others. It focuses on the direct modeling and counting strategies. For example the whole is an unknown number. For an exercise you can ask the questions like There are two boys and six girls. How many children in all are there?
What are the Big Ideas about Number Operations?
One big idea about number operations is that a quantity (whole) can be decomposed into equal or unequal parts; the parts can be composed to form the whole. Sets can be compared to by using the attribute of numerosity, and ordered by more than, less than, and equal to. Lastly sets can be changed by adding items together or by taking them away from a group or set.
What are factors that affect difficulty?
Some factors that affect difficulty are students making sense of "naked numbers". This is hard for students to grasp because if they haven't been taught and exercise the questions like how much? Is there fewer, or more? Students need concrete experiences with numbers in order to understand that they represent quantity. It is important that they practice sets and understand that the sets represent a quantity and when they are combined the number becomes larger or represent more quantity. In order to prevent math difficulty for students they must understand and have lots of experience with smaller numbers. Another form of difficulty is seen in kindergarteners with unknown change or unknown start. It is hard for them to understand the part/whole relationships with numbers that are in a set which are more difficult to “act out.” Lastly language issues makes comparison difficult for some students. Comparisons can be formed in many different ways in a problem. For example, 8 is more than 6; 6 is less than 8. Children are more interested in questions like what is more or bigger. They find it more complex to understand with comparison of two numbers, this reluctance seems to be carried over into mathematics in their later years.
Watch this: https://www.youtube.com/watch?v=PUY072JHE4g
Chapter 5
Read the entire chapter. Highlight the information that stands out to you.
Define the following terms and give an example for each:
repeating patterns- these types of patterns contain a segment that repeats continuously. The segment is called unit of repeat. This type of unit can vary in length and level of complexity. The unit of repeat is what governs the rule of patterns. For example a pattern is something that is predictable and can be guessed on knowledge of what is included in the pattern. If it is something that repeats in the same order then it can be considered a pattern.
temporal pattern- is a type of pattern that include hours and minutes, they days of the week or the seasons. An example of a temporal pattern would be the calendar.
growing patterns- are patterns that increase or decrease by a constant amount. When students work with repeating patterns they gain more of an understanding of growing patterns. An example of growing patterns would include the basic growing pattern in our counting system 1,2,3,4,5...
concentric patterns- include circles or rings that grow from a common center. An example of this would be if you threw a pebble into water and it created a ripple effect.
movement patterns- is a type of pattern that involves scaffolding in order for children to extend patterns with support from others. The multiple modalities of the activity help children understand the math by using their hands, eyes, ears, and feet. The goal of movement patterns is to teach students to recognize how patterns can grow and be extended.
Give 5 examples of how you can see patterns in a everyday classroom.
One way to explore patterns in the classrooms by the routines that are integrated in their everyday life. Each student can talk about their daily schedule and can see if there are patterns in their every day lives For example eating breakfast then coming to school, having class, go to lunch, recess, go home, have dinner, get ready for ed, then go to sleep.
another way to talk about patterns in the classroom is by doing the activity called people pattern which gives the students the chance to engage in creating their own patterns. For example they can ask the kids in the class to sit, stand, sit, stand, sit and stand. This is a great opportunity to have them talk and explain why this is a pattern and what its rule is.
There are maybe children that might be wearing something that has a pattern like jewelry or a shirt. You could use the manipulative of patterns in the classroom at any time. Also, it is effective to compare patterns and ask the question "how are these patterns alike" or "how are they different". This helps the student notice attributes about shapes and size.
Another use of patterns in the classroom is in the students artwork. Art provides materials like multiple colors and textures. Stamps and stencils are manipulatives that are easy to repeat.
Outside on the playground is a fun way to find patterns in nature. This can expand children's mind to realize that patterns aren't always man made and they can occur everywhere. For example, they can listen to the birds calls or look at flower petals and try to find a pattern. Another way to find patterns outside is to use the playground. For example, swings going back and forth or a ball bouncing up and down.
Chapter 6
Read the entire chapter. Highlight the information that stands out to you.
Define the following terms and give an example for each:
capacity- is a unit of measurement that measures the size of the inside of containers. For example, a student might find out the compacity of containers by pouring water into it and seeing which one fills up faster or holds more water. An example of compacity is how much a container holds or the amount in which a container holds.
unit- is a crucial measuring component, these units are in other words, inches, pounds, and ounces. These are not things or objects but a unit of measurement. One way to get kids started with measurement is to use nun-standard objects. They can use tools such as the "adding machine strips" in other words a tape measurer.
fair comparison- all measurements involves a fair comparison. There has to be a fair comparison when measuring individual attributes. Therefore there needs to be an understanding of the nature of the attribute being measured. An example of fair comparison would be to have the student make a paper "foot" and compare their foot to things posted on the wall. Another example would be to have the students compare the length of their hand and find things that are the same size.
Search the internet for activities that involve measurement for kindergarten students. Share 3 activities on your Google Site. Add the links to your resources.
Fun Math Game for Kids | Teach Kids to Use Measuring Cups (wpcomstaging.com)
Watch this: https://www.youtube.com/watch?v=nuYWIM4_S-o