What is 21st Century Learning?
Definition: The term 21st century skills refers to a broad set of knowledge, skills, work habits, and character traits that are believed—by educators, school reformers, college professors, employers, and others—to be critically important to success in today’s world, particularly in collegiate programs and contemporary careers and workplaces. Think jobs that have yet to be thought of or created.
I have talked throughout the year about how my district has encouraged the 4Cs in all my planning. It has driven how I created my students Personalized Learning Pathways (PLP) for my students—they have IEPs.
You know the four Cs right. Great colors, wonderful wording and multiple ways to explain:
- Communication
- Collaboration
- Creativity
- Critical Thinking
Problem solving
Students need the ability to solve complex problems in real time.
Why it’s important: In the future, complex problems that we can’t even conceive right now will be everywhere. The more we focus on students’ ability to devise effective solutions to real-world problems, the more successful those students will become.
Creativity
Students need to be able to think and work creatively in both digital and non-digital environments to develop unique and useful solutions.
Why it’s important: Our digital students are in a constant state of stimulation and neural development with technology use. They are natural producers and consumers, or prosumers, of information. Problem-solving is a skill that comes naturally to them and this can be advanced profoundly with the proper engagement in their learning. This comes from doing rewarding projects and meaningful tasks that give them challenges to overcome in imaginative ways.
Analytic thinking
Students need the ability to think analytically, which includes proficiency with comparing, contrasting, evaluating, synthesizing, and applying without instruction or supervision.
Why it’s important: Analytic thinking means being able to use the higher end of Bloom’s Digital Taxonomy or higher-order thinking skills (HOTS).
Collaboration
Students must possess the ability to collaborate seamlessly in both physical and virtual spaces, with real and virtual partners globally.
Why it’s important: Students of the digital age are social by nature. They text, post, update, share, chat, and constantly co-create in technological environments with each other. When they are unable to do this in school, they become disengaged and unattached to their learning. Connection and collaboration with others are essential not only to their learning but their mental and emotional health. This kind of interaction goes hand-in-hand with the mindset of global awareness that is part of Global Digital Citizenship. Simply put, better collaborators make better students—and better citizens.
Communication
Students must be able to communicate not just with text or speech, but in multiple multimedia formats. They must be able to communicate visually through video and imagery as effectively as they do with text and speech.
Why it’s important: Communication is a broad term that incorporates multi-faceted levels of interaction and sharing information. Students love to communicate using technology. But it’s more than just being able to effectively use digital media. It’s about personal interactions as well.
What does this mean my Resource Room?
In my world, it’s about pushing students’ thinking with Higher Order Thinking Skills—think Create or Evaluate (Old Bloom’s), Synthesis or Evaluation (New Bloom’s), or Depth of Knowledge Level 4—Extended Thinking).
I do this with more than thinking critically about a book. With each book or group of books (depends on reading level) students have an Essential Question. This question encourages then to think beyond the text and create new information based on what they have learned. This question becomes the starting point of their PLP. They have voice and choice in how they answer the essential question. You also have to realize the work leading up to them creating their answer maybe anywhere from a couple of days to a whole month. I see students 4 days a week for at least 30 minutes a day. Most of
them are students with learning disabilities, communication delays or students with Autism. Students only get at the MOST a couple of days to do their work—that time is theirs’s; not mine. I’m a guide, a support, techno wiz, troubleshooter, ear, problem solver but not teacher or answer giver. They do all the work. I’m really looking forward to seeing how their work with the new version I created with App-Smashing instead of one app for each of the 4C’s. Plus, we are moving everything second semester over to Seesaw (which I hope is way more user friendly to share work with parents, peers, and families. I'll post ideas and project on how I make all this work and meet IEP goals in the coming year.
December Show and Tell
This year my big goal has been looking for ways to bring a little bit of tech into what we are doing. For the pieces I have added to the room I do most if not all of the work. This in most cases would not be a problem but with my teacher's rubric and the need for students to show what they have learned and apply it--this is a huge problem.
My break so far has been looking at different ways student can take these ideas and run with them.
For the record I do everything in google. I put student work in Drive. I take the photos and upload the work. To be fair this is because I don't have local control of the iPads in my room. Yes, I know but I have had to create work arounds for everything we do. I came across Seesaw and was impressed with the idea that it is student and time friendly. I only have my groups for about 30 minutes. This means I either need to do it when I have a 2 minutes or they need to do the up-loading and creating within that 30 minutes. I love the app options that can be uploaded into the platform. My hope is this is REALLY student friendly and will become a place students can create and show off their app-smashing.
My district is big on redefinition--this is seen in the teacher rubric to score highly effective I have to create opportunities for students to "Create and Evaluate" what they have learned.
I have two groups that are working on Non-Fiction Text Features. This will be the first Aurasma, I'm going to show my students. I've been working on how to do this because let's be honest I have no idea and if I'm going to share and have them do the same I better figure it out. Crossing my fingers it works! More coming on this soon.
Merry Christmas and Happy New Year!
Letter-Sound Correspondence
What are letter-sound correspondences?
Letter-sound correspondences involve knowledge of:
- the sounds represented by the letters of the alphabet
- the letters used to represent the sounds
Why is knowledge of letter-sound correspondences important?
Knowledge of letter-sound correspondences is essential in reading and writing
- In order to read a word:
- the student must recognize the letters in the word and associate each letter with its sound
- In order the student must break the word into its component sounds and know the letters that represent these sounds.
What sequence should be used to teach letter-sound correspondence?
Letter-sound correspondences should be taught one at a time. As soon as the student acquires one letter sound correspondence, introduce a new one.
I tend to teaching the letters and sounds in this sequence
- a, m, t, p, o, n, c, d, u, s, g, h, i, f, b, l, e, r, w, k, x, v, y, z, j, q
- Letters that occur frequently in simple words (e.g., a, m, t) are taught first.
- Letters that look similar and have similar sounds (b and d) are separated in the instructional sequence to avoid confusion.
- Short vowels are taught before long vowels.
- I tend to teach lower case letters first before upper case letters. Pick one and stick to it.
- prior knowledge
- interests
- hearing
Start by teaching the sounds of the letters, not their names. Knowing the names of letters is not necessary to read or write. Knowledge of letter names can interfere with successful decoding.
- For example, the student looks at a word and thinks of the names of the letters instead of the sounds.
The student will:
- listen to a target sound presented orally
- identify the letter that represents the sound
- select the appropriate letter from a group of letter cards, an alphabet board, or a keyboard with at least 80% accuracy
Instructional Task
Here is an example of instruction to teach letter-sound correspondences
Teacher
- introduces the new letter and its sound
- shows a card with the letter m and says the sound “mmmm”
After practice with this letter sound, the instructor provides review
Teacher
- says a letter sound
- listens to the sound
- looks at each of the letters provided as response options
- selects the correct letter
- from a group of letter cards,
- from an alphabet board, or
- from a keyboard.
Instructional Materials
Various materials can be used to teach letter-sound correspondences
- cards with lower case letters
- an alphabet board that includes lower case letters
- a keyboard adapted to include lower case letters
- listen to the target sound – “mmmm”
- select the letter – m – from the keyboard
Instructional Procedure
The teacher teaches letter-sound correspondences using these procedures:
- Model
- The teacher demonstrates the letter-sound correspondence for the student.
- Guided practice
- The teacher provides scaffolding support or prompting to help the student match the letter and sound correctly.
- Independent practice
- The student listens to the target sound and selects the letter independently.
- The teacher monitors the student’s responses and provides appropriate feedback.
Pointers
There are a wide range of fonts. These fonts use different forms of letters, especially the letter a.
- Initially use a consistent font in all instructional materials (I use one that have the capital I and lower case q-I want.)
- Later, I introduce variations in font.
What is Effective Comprehension Instruction?
It is Explicit, Intensive, persistent instruction. I do mine in small and large groups. Small groups allow me to focus in on the specific skill the groups needs. I find this is a great easy way to differenate students because each student does not need to be in the same reading material--they are grouuped to practice the specific comprehension skill.
To become good readers, most students require explicit, intensive, and persistent instruction. In explicit comprehension strategy instruction, the teacher chooses strategies that are closely aligned with the text students are reading. The teacher models and "thinks aloud" about what a given strategy is and why it is important, helps students learn how, when, and where to use the strategy, and gives students opportunities to apply the strategy on their own.
Modeling is followed by practice, guided by the teacher, who works with students to help them figure out how and when to use the strategy themselves. As students read, the teacher provides feedback and engages them in discussion. In subsequent lessons, the teacher asks students to apply the strategy on their own to other texts.
Students are encouraged to plan before reading so that reading has a clear goal or purpose, to continually monitor their understanding during reading, and to apply repair strategies when breakdowns in understanding occur. To improve self-monitoring, the teacher may model for students how to do one or all of the following:
· think about what they already know before they start reading and during reading;
· be aware of whether they understand what they are reading;
· employ strategies to identify difficult words, concepts, and ideas;
· ask themselves: "Does this make sense?"; and
· be aware of how a particular text is organized.
One of the most important features of explicit instruction is the teacher's gradual release to students of responsibility for strategy use, with the goal that students apply strategies independently. However, teachers do not ask students to work on their own until the students have demonstrated that they understand a strategy and how and when to use it.
The Primary Comprehension Toolkit from Heinemann (grade K-2) allows me to teach specific comprehension skills in a sequence that makes sense to the reader. The student does the work--I have to listen to how they are applying the strategies to text.
My students LOVE expository text (non-fiction). Most of the reading students do throughout their schooling — indeed, throughout their lives — will involve expository text. Without an understanding of the organization of such text, students often have difficulty understanding what they read. Unlike a narrative, an expository text has no familiar story line to guide students' reading. To read expository texts successfully, students must learn that authors may use a variety of structures to organize their ideas, including cause-and-effect or compare and contrast relationships, time-and-order sequences, and problem-solution patterns. Indeed, students need to know that authors may use some or all of these structures in any given chapter or section of a text.
They need to learn that expository text can differ from narrative text in the way it is presented on a page. For example, expository text may be organized by means of text headings and subheadings, and may contain extensive graphics, such as tables, charts, diagrams, and illustrations. Instructional practices that facilitate students' understanding of expository text include helping them learn how to:
· chunk information in a text by grouping related ideas and concepts;
· summarize important information in a text by grouping related ideas and concepts;
· integrate information in a text with existing knowledge;
· apply information in a text to real-world situations;
· interpret and construct graphics such as charts, tables, and figures;
· synthesize information from different texts; and
· develop presentations about the text
and this one show two examples of the sentence stems.
My hope in using the Primary Comprehension Toolkit is to have student's think more critically about what they have read to in turn create new works that show how they created meaning strategically in reading and writing. This set of strategies being tied to their Personalized Learning Plans. I hoping to see great products but I'll have to wait until next week to see what students do.
Teachers pay Teachers Gift Card Give Away
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And after the turkey and special time together draws to a close, please join in throwing a great, big, magnificent Cyber Monday Sale. Earlier this week, I was sent a Teachers pay Teachers $10 gift card for the Cyber Monday and Tuesday sale. To help with the shopping, you have a chance to win a gift card. With 4 chances and a winner picked before the sale gets going-all you have to do is shop.
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Classroom Accommodations Ideas
If the student has difficulty learning by listening, then try…
Before the lesson:
- Pre-teach difficult vocabulary and concepts
- State the objective, providing a reason for listening
- Teach the mental activities involved in listening — mental note-taking, questioning, reviewing
- Provide study guides/worksheets
- Provide script of film
- Provide lecture outlines
During the lesson:
- Provide visuals via the board or overhead
- Use flash cards
- Have the student close his eyes and try to visualize the information
- Have the student take notes and use colored markers to highlight
- Teach the use of acronyms to help visualize lists (Roy G. Biv for the colors of the spectrum: red, orange, yellow, green, blue, indigo, violet)
- Give explanations in small, distinct steps
- Provide written as well as oral directions
- Have the student repeat directions
- When giving directions to the class, leave a pause between each step so student can carry out the process in his mind
- Shorten the listening time required
- Provide written and manipulative tasks
- Be concise with verbal information: "Jane, please sit." instead of "Jane, would you please sit down in your chair."
- If the student has difficulty expressing himself verbally, then try…
To accept an alternate form of information sharing, such as the following:
- Written report
- Artistic creation
- Exhibit or showcase
- Chart, graph, or table
- Photo essay
- Map
- Review of films
- Charade or pantomime
- Demonstration
- Taped report
- Ask questions requiring short answers
- Provide a prompt, such as beginning the sentence for the student or giving a picture cue
- Give the rules for class discussion (e.g., hand raising)
- Give points for oral contributions and preparing the student individually
- Teach the student to ask questions in class
- Specifically teach body and language expression
- Wait for students to respond — don't call on the first student to raise his hand
- First ask questions at the information level — giving facts and asking for facts back; then have the student break in gradually by speaking in smaller groups and then in larger groups
If the student has difficulty reading written material, then try…
- Find a text written at lower level
- Provide highlighted material
- Rewrite the student's text
- Tape the student's text
- Allow a peer or parent to read text aloud to student
- Shorten the amount of required reading
- Look for same content in another medium (movie, filmstrip, tape)
- Provide alternative methods for student to contribute to the group, such as role playing or dramatizing (oral reading should be optional)
- Allow extra time for reading
- Omit or shortening the reading required
- Substitute one-page summaries or study guides which identify key ideas and terms as the reading assignment
- Motivate the student, interesting him
- Provide questions before student reads a selection (include page and paragraph numbers)
- Put the main ideas of the text on index cards which can easily be organized in a file box and divided by chapters; pre-teaching vocabulary
- Type material for easier reading
- Use larger type
- Be more concrete-using pictures and manipulatives
- Reduce the amount of new ideas
- Provide experience before and after reading as a frame of reference for new concepts
- State the objective and relating it to previous experiences
- Help the student visualize what is read
If the student has difficulty writing legibly, then try…
- Use a format requiring little writing
- Multiple-choice
- Programmed material
- True/false
- Matching
- Use manipulatives such as letters from a Scrabble™ game or writing letters on small ceramic tiles
- Reduce or omit assignments requiring copying
- Encourage shared note-taking
- Allow the use of a tape recorder, a typewriter, or a computer
- Teach writing directly
- Trace letters or writing in clay
- Verbalize strokes on tape recorder
- Use a marker to space between words
- Tape the alphabet to student's desk
- Provide a wallet-size alphabet card
- Provide courses in graph analysis or calligraphy as a motivator
- Use graph paper to help space letters and numbers in math
- Use manuscript or lined ditto paper as a motivation technique (brainstorm the advantages of legibility with the class)
If the student has difficulty expressing himself in writing, then try…
Accepting alternate forms of reports:
- Oral reports
- Tape-recorded report
- Tape of an interview
- Collage, cartoon, or other art
- Maps
- Diorama, 3-D materials, showcase exhibits
- Photographic essay
- Panel discussion
- Mock debate
- Review of films and presentation of an appropriate one to the class
- Have the student dictate work to someone else (an older student, aide, or friend) and then copy it himself
- Allow more time
- Shorten the written assignment (preparing an outline or summary)
- Provide a sample of what the finished paper should look like to help him organize the parts of the assignment
- Provide practice using:
- Story starters
- Open-ended stories
- Oral responses (try some oral spelling tests)
If the student has difficulty spelling, then try…
- Dictate the work and then asking the student to repeat it (saying it in sequence may eliminate errors of omitted syllables)
- Avoid traditional spelling lists (determine lists from social needs and school area needs)
- Use mnemonic devices ("A is the first capital letter," "The capitol building has a dome")
- Teach short, easy words in context:
- On and on
- Right on!
- On account of
- Have students make flashcards and highlight the difficult spots on the word
- Give a recognition level spelling test (asking the student to circle correct word from three or four choices)
- Teach words by spelling patterns (teach "cake," "bake," "take," etc. in one lesson)
- Use the Language Master for drill
- Avoid penalizing for spelling errors
- Hang words from the ceiling during study time or posting them on the board or wall as constant visual cues
- Provide a tactile/kinesthetic aid for spelling (sandpaper letters to trace or a box filled with salt or cereal to write in)
This is just the tip of the iceberg of ideas to use in the classroom. What are your favorites?
Ideas in Selecting "Just Right" Books
One of the hardest thing to help students understand is choosing a "Good Fit" book. Here are some ideas how I work with students and parents to have students in a "Good Fit" book more times than not.
Students choose books for independent reading for many different reasons: “I just saw the movie,” “I like the pictures,” “My friend just finished it.” Students usually choose books that appeal to them visually. The front covers are designed to capture their interest and emotions. However, many students do not choose a book that they can actually read independently and with success.
A teacher or parent can provide feedback by matching the book to the reader. This can be done by having the student read aloud while the teacher listens and records the miscues. Typically, I count the errors on a page. If it’s more than five-the book is too hard.
If the book is too difficult, it will lead to frustration; too little of a challenge will lead to boredom. So the book needs to be “just right.” A just right book is one that provides a little bit of a challenge for the student. It should be a book that the student finds interesting and can be read with a small amount of assistance with the text. Spending time reading just right books during independent reading time will help students become stronger.
It would be acceptable, occasionally, for a student to choose a slightly difficult book they are interested in a specific subject and finds a difficult book that centers on this subject. However, providing a steady diet of books that are too difficult for the student will cause more harm. The student needs to understand and enjoy the book for reading success. Many students who choose hard books give up on the book out of frustration.
Reading lots of easy books will build confidence and fluency. Pattern books, predictable stories, and familiar books will provide the student with the opportunity to work on building a level of comfort and self-reliance. Reading fluency and comprehension are linked. Students who spend a great deal of energy on decoding lose all meaning of the story. A student who has difficulty with fluency may have been reading at a frustration level for quite some time. Finding the right level of books for this student is essential. Matching the book to the reader will provide an opportunity for the student to read with comprehension and relative ease. Reading is about gaining meaning, so students should be reading manageable texts and understanding what they read.
Easy books allow students to focus on the meaning and think deeper about characters and plot. However, too much easy reading will not promote growth in reading. This is when teacher input is vital. Observing the students closely and monitoring their progress will give the teacher the information to move the student gently to more difficult books. As the student moves to just right books, he or she will continue to develop reading skills. The text should be challenging enough to allow the student to work out problems or learn a new strategy.
A just right book is a book the student finds interesting and can confidently read and understand with
a small amount of support. These books also make the student stretch a little bit so that they have opportunities to apply the strategies they have been learning and to experience new vocabulary and different genres.
Another way to help students choose an appropriate book is to teach them about the “Goldilocks” strategy. This strategy has three categories: Too Hard, Just Right, and Too Easy. The students answer several questions for each category. If the answers are “yes,” the book probably fits into that category. Modeling this strategy for students will help them understand before they have to apply it independently. This strategy has been modified from its original to meet the needs of primary students.
Too Easy
Just Right
Too Hard
Developing criteria with your students for choosing a just right book is an additional effective activity. Students develop the guidelines along with the teacher. This can be accomplished during a shared writing activity. Students naturally include enjoyment and understanding as items on their list. The criteria can be listed on a chart and kept in a prominent spot as a reminder.
Choosing books that are just right for students and teaching them how to choose for themselves is an essential piece of a successful reading program. Struggling readers as well as successful readers need to have the opportunity to practice what they have learned. Teachers have the opportunity to make this happen in their classrooms. Choosing books that are appropriate for students involves many various considerations. Student interest, reading purpose, and reading level are just a few of those considerations. Independent reading combined with read-alouds, shared reading, and guided reading can provide students with a variety of experiences. Students benefit from daily opportunities to read books they choose for themselves for their own purposes and pleasures.
Students choose books for independent reading for many different reasons: “I just saw the movie,” “I like the pictures,” “My friend just finished it.” Students usually choose books that appeal to them visually. The front covers are designed to capture their interest and emotions. However, many students do not choose a book that they can actually read independently and with success.
A teacher or parent can provide feedback by matching the book to the reader. This can be done by having the student read aloud while the teacher listens and records the miscues. Typically, I count the errors on a page. If it’s more than five-the book is too hard.
It would be acceptable, occasionally, for a student to choose a slightly difficult book they are interested in a specific subject and finds a difficult book that centers on this subject. However, providing a steady diet of books that are too difficult for the student will cause more harm. The student needs to understand and enjoy the book for reading success. Many students who choose hard books give up on the book out of frustration.
Reading lots of easy books will build confidence and fluency. Pattern books, predictable stories, and familiar books will provide the student with the opportunity to work on building a level of comfort and self-reliance. Reading fluency and comprehension are linked. Students who spend a great deal of energy on decoding lose all meaning of the story. A student who has difficulty with fluency may have been reading at a frustration level for quite some time. Finding the right level of books for this student is essential. Matching the book to the reader will provide an opportunity for the student to read with comprehension and relative ease. Reading is about gaining meaning, so students should be reading manageable texts and understanding what they read.
Easy books allow students to focus on the meaning and think deeper about characters and plot. However, too much easy reading will not promote growth in reading. This is when teacher input is vital. Observing the students closely and monitoring their progress will give the teacher the information to move the student gently to more difficult books. As the student moves to just right books, he or she will continue to develop reading skills. The text should be challenging enough to allow the student to work out problems or learn a new strategy.
What to do:
Children need to learn how to choose a book. Giving them the opportunity to choose from a small group of books is a beginning. Modeling how to look through a book--looking at the cover, flipping through the pages, and scanning the illustrations--will provide students with an excellent example. Many teachers explain the five-finger rule to their students. This rule reminds students to count on their fingers every time they miss a word in a particular book. If they miss five words, the book may be too hard. If they miss three words or fewer, it might be “just right”.A just right book is a book the student finds interesting and can confidently read and understand with a small amount of support. These books also make the student stretch a little bit so that they have opportunities to apply the strategies they have been learning and to experience new vocabulary and different genres.
Another way to help students choose an appropriate book is to teach them about the “Goldilocks” strategy. This strategy has three categories: Too Hard, Just Right, and Too Easy. The students answer several questions for each category. If the answers are “yes,” the book probably fits into that category. Modeling this strategy for students will help them understand before they have to apply it independently. This strategy has been modified from its original to meet the needs of primary students.
Too Easy
- Have you read it lots of times before?
- Do you understand the story very well?
- Do you know almost every word?
- Can you read it smoothly?
Just Right
- Is the book new to you?
- Do you understand a lot of the book?
- Are there just a few words on a page you don’t know?
- When you read, are some places smooth and some choppy?
Too Hard
- Are there more than five words on a page you don’t know?
- Are you confused about what is happening in most of this book?
- When you read, does it sound choppy?
- Is everyone else busy and unable to help you?
Developing criteria with your students for choosing a just right book is an additional effective activity. Students develop the guidelines along with the teacher. This can be accomplished during a shared writing activity. Students naturally include enjoyment and understanding as items on their list. The criteria can be listed on a chart and kept in a prominent spot as a reminder.
Choosing books that are just right for students and teaching them how to choose for themselves is an essential piece of a successful reading program. Struggling readers as well as successful readers need to have the opportunity to practice what they have learned. Teachers have the opportunity to make this happen in their classrooms. Choosing books that are appropriate for students involves many various considerations. Student interest, reading purpose, and reading level are just a few of those considerations. Independent reading combined with read-alouds, shared reading, and guided reading can provide students with a variety of experiences. Students benefit from daily opportunities to read books they choose for themselves for their own purposes and pleasures.
October Show and Tell
I love putting things in pictures. Pictures move faster to the brain than words. This one has become our Problem Solving Rubric which shows not tells students what is needed to score a 3 on the rubric. Problem Solving is one skill I want students' to take back to the classroom. The picture helps remind them what it needs to look like.
Book Tasting any one? This was how students' showed they created meaning from what they read. We even shot videos that show them out at a picnic. The fun they created with a green screen. It was amazing to see what they liked and disliked about what they read. The picture was the hardest (yes, the hardest) thing for them to create as it needed to show something from what they read.
This month has been about putting in place systems. I have two groups moving more towards being a grade level and need more time to work in a rotation schedule. In their time with me, they will over a week work through three stations plus guided reading. As they also need to have time to show how they create meaning strategically in what they are reading with each book. We'll see-this could be a big fail.
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This week I joining the party celebrating Michelle Dupuis's new Teacher pay Teacher store. She how has her English materials in one store and French in the other. We are giving away Four (Yes 4) TpT gift cards ($50, $50, $25, $25).Be sure to enter in both Rafflecopters.!
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Best Practices: Number Sense
A sense of numbers is critical for primary students to develop math problem solving skills.
The National Council of Teachers of Mathematics increasingly calls for districts to give more attention to building this skill, and studies have found that number sense accounts for 66% of the variance in first grade math achievement. The council have also addressed five critical areas that are characteristic of students who have good number sense:
- Number Meaning
- Relationships Between Numbers
- Number Magnitude
- Operations Involving Numbers
- Referents for Numbers/Quantities (referents are words or phrases that denote what something stands for)
WHAT IS NUMBER SENSE IN CHILDREN?
Having a sense of how numbers work is a very broad topic that covers all numerical thinking. At its core, it is making sense of math concepts and mathematical reasoning.
Operationally, it is counting skills, having number knowledge, using estimation, and the ability to use problem solving strategies.
Knowing the why of how numbers work is of utmost importance, and children should not be shown the how until they understand the "why." Techniques such as using ten frames and using concrete models to show place value concepts are daily necessities for young children.
Inquiry-based approaches (such as math dice games) to teaching children mathematics should be utilized as primary teaching methods in the early grades.
This is not to say that explicit teaching of sense of numbers skills is not essential, especially for those students from low socio-economic status. We absolutely need to do this.
It is saying that teachers should provide multiple opportunities for students to experience numbers and make connections before putting the pencil to paper.
Carefully consider your objectives and the type of learners in your room when choosing a math game to include. NCTM also suggests you consider:
- the type of mathematical practices involved in each game (there should be more than one)
- how feedback will be given
- does the game encourage competition, collaboration and communication?
- the types of strategies students will have to use to solve a puzzle or to win
Seven ways teachers can directly impact a developing sense of number.
1. Link school math to real-world experiences
Present students with situations that relate to both inside and outside classroom experiences. Students need to recognize that numbers are useful for solving problems.
2. Model different computing methods
Focus on what methods make sense for different situations. There is no one right way to compute. We need our students to be flexible thinkers.
3. Mental Math
Real life requires mental computation. Students need to be able to move numbers around in their heads and discuss their strategies.
4. Discuss Strategies
Students must be able to explain their reasoning. This not only will give you insight into how they think, but also will help the children to cement their own ideas and reevaluate them.
5. Estimate
This should be embedded in problem solving. This is not referring to textbook rounding. Real life estimation is about making sense of a problem and using anchor numbers to base reasoning on.
6. Question Students About Reasoning Strategies
All the time, not just when they make a mistake. Constantly probing sends several important messages: your ideas are valued, math is about reasoning, and there are always alternative ways to look at a problem.
7. Measuring Activities
When teaching children mathematics, measuring activities should be front and center. Make students verify estimates through doing.
September Show and Tell
I'm linking up for this month's view into my classroom with"Forever in 5th Grade's" Show and Tell.Student's have been back for 30 some odd days. Most of our time in small groups has been spent building routines and learning how "Parts to Whole" can help us read and write.
An important thing for student's is they need to show how each of them created meaning strategically of the digraphs. These guys have spend the last couple weeks learning and working with digraphs in reading and writing. The point is to get them to use higher order thinking to demonstrate how they created meaning i.e-how will they remember them as they move on to more complicated reading and phonics work.
Each group has it's own fluency challenge. From letter names to high frequency words a differentiated fluency game based on the same idea. Even with spending most of our time on phonics, spelling and reading have to be a fluency practice. My groups beg, for time to do "Up Against the Wall." I've put the data on the wall next to the posters using their data binder numbers. My hope is that by working on sight words their grade level oral reading scores will increase. (By this spending less time on them as a whole.)
I have decided to take the big step to move my lesson planning to Google. This is week 3 and I LOVE it. I have Google Slides Lesson Plans for each group. Each week I make a copy of the plan and make my changes. I can take pictures of student work and up-load it to their file. It does help students have binders they keep everything in guided reading books, their data, everything.
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