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Personally, I really don't like any curriculum being so structured. Not being able to have some wiggle room is a really bad thing, because no two students are the same, and no two classes have the same needs. There should always be, in my opinion, some leeway on behalf of the teachers. They might even have to completely change the activities or time frame of a lesson in order to better serve their students. My current curriculum has me teaching my kindergarteners the numbers 1-5 all in one day, and I have to adjust that to cover one or two numbers a day, because it is overwhelming. The activities have to be changed too, as not all of my students can do or even benefit from completing a worksheet.

I agree with you in that the curriculum structure has no wiggle room for us to use with our students with disabilities. I often find myself teaching one topic for three days that the curriculum has us teaching in just one day. -Paola German

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I am not a fan of a structured curriculum. I believe that a curriculum should not go by the state standards, it should go by the students' standards, as to not go ahead of where the students are comfortable in math.

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by Miaochang Lin

I agree that some students struggle with mathematic maybe driven by difficulty with language. Those students may present with challenging vocabulary, since some of the terminologies are rarely heard or use outside of the math classroom. Therefore, those students experience difficulty when they are trying to understand word problems and use language in math for tasks such as explaining their answers.

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By Miaochang Lin
Some students think math is a bore. We can find many printable worksheets and online math games to make learning math fun. Children are excited when they are playing games in the classroom. Therefore, we can help them practice math skills in exciting game formats, such as learning algebra with destroying zombies (plants vs. zombies) or rescuing animals.

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I found the part about "the written symbol system and concrete materials" very interesting. Garnett talks about how some students who seem to struggle with math actually already have a strong informal understanding of math, but struggle to see how this related to the formal structures of school math. This makes me reflect on how as teachers we must really work to understand conceptual math ourselves, so we can understand our students' ideas about math even if they express them in an unconventional way. I recently did math interview assessments with my second grade class. One student was doing very well overall and seems to have lots of ways of authentically understanding math for herself. But on a question where I asked her to create a story problem that would match "5 + 13 = 18," she got stuck. Reflecting on this and her overall performance, I really don't think this student lacks conceptual understanding of division. I think she just didn't understand the school-centric question I was asking her.

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I think often classroom teachers encourage "equality" or every student getting the same instruction which is not actually giving all students what they need. A classroom that serves all of its students doesn't look very orderly, students may be using different materials, methods, and modes of working in order to achieve learning. It can be hard to tolerate as a teacher who seeks order, but it is necessary to invite and encourage this type of environment in order to create a classroom that achieves "equity."

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One of the major challenges when it comes to math disorders is the ability to memorize basic number facts. From counting to multiplication we learn basic number facts in early elementary curriculum. At this point in mathematics, a student can fall far behind. Often we are taught memorizing number facts by drilling in facts. This can be with flashcards or fact quizzes. Yet, students who struggle with memorization will struggle to memorize number facts. We need to not only drill these facts into students but show alternate ways as to why this is the answer. For example, how can addition relate to multiplication and how can multiplication relate to division. If in the 4th grade a student hasn't mastered their number facts, by the time they are in 6th grade they are expected to know and become lost as the material moves at a quicker pace while using those number facts in formulas. How can a student who never mastered their multiplication facts be able to understand and keep up when we start throwing letters and numbers together into equations. These students will have difficult times with understanding math and will form poor relations of frustration to the material.

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I think that schools need to start creating math groups of students of the same math level, instead of general math classes where students can be of varying low math levels, varying middle math levels, or varying high math levels. I don't believe students need to be held back, but I do believe that students should not be pushed and they should fully understand every part of math before moving onto the next part. I don't like the idea of having a pocket cheat sheet because that implies to me that they just don't understand what is going on in the math class.

Response from Jamice Miller: Jessica, I do agree about having some form of differentiation in math groups simply because students feel left out and begin to check out due to the lesson not being accessible to them. When I think of pocket cheat sheets, I think of multiplication charts, formula cards, etc. I think those are great for students because when entering testing grades, they usually are asked for strategy AND the correct answer. If students are solely focused on the right answer, they tend to get anxious but if they have a formula sheet they'll be able to solve multiple problems and check where they may have miscalculated in the problem.

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As a current special education teacher, all my students have IEP's meaning they do not all follow the same curriculum or are at the same grade levels. I think that using a structured curriculum can sometimes be tricky for students with learning disabilities because they may not be learning at the same pace as the curriculum flows. They may need extra time on specific subjects that might take longer than planned if following a curriculum. This would put pressure on students as well as teachers to rush through topics when the information is not fully learned or understood.

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Students use math at a young age in play, by teaching math with use of common objects, a student can make the connection between the concept and the algorithm. When a student understands math. I am teaching my students now about patterns that make up six (addends of six). Using unifix cubes which are essentially blocks, to dominos and then bridge that understanding to fact families, a student can understand math through a language they already are familiar with! They then can apply that understanding with real life experiences (buying a hot cocoa with money, making sure they have enough markers or pencils for the day). See attach for a sample worksheet I am doing with my students.

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Kate Garnett speaks about the complex balance of a math teacher. A teacher must recognize a student's computational weakness, strengthen inconsistent skills, and become partners with the students to give them the tools they need to succeed, WHILE engaging in the scope of math teaching! By engaging in repeated practice and integrating past skills with the new (going from the known to the unknown), a student develops a sense of trust in the math process and begins to understand the interconnectivity of math.

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We must teach math as a second language.

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We must teach math as a second language.

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By: Perry Moskowitz

When it comes to learning mathematics, I believe children are faced with troubles and bumps in the road. This is extremely true in children with various disabilities. As we have learned before math is a language and the students need to be proficient in basic math before technically moving on and learning harder equations. Kate Garnett stated this issue as well, children with reading disabilities also have trouble processing the information and reading the issue at hand sequentially. Math is happening all around us, and we have to teach children why it is important. Math is like a second language!

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There are a lot of challenges when it comes to learning mathematics for students with disabilities. From the article, it discussed how many students with reading disabilities also have trouble processing math concepts. People who struggle with learning math can cause them serious struggles in every day life such as making change at the grocery store, reading signs with numbers on them, struggles with learning time and many more struggles.

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By: Katie Donohue
Interactive play certainly has its place in the classroom. Instead of our students dreading math instruction, because it lacks things like literacy’s Reader’s Theatre and science’s endless experiments, we should up our game as teachers and create these fun learning opportunities in math so that our students are making more positive associations with the subject. Since we know that so much success comes to our students who struggle more with math from using manipulatives and having something concrete to make things make sense, we should build off of that. While majoring in psychology, one of my professors recommended changing up our study locations to promote better recall, as it forces the brain to make multiple associations with the same material, strengthening those neural connections! I believe that this could be generalized to include interactive play, so I went searching for some fun games to play in a math class. One game that I really liked was “Simon Says: Geometry” on Scholastic, where students are instructed to make different angles with only their arms, parallel lines, perpendicular lines, obtuse, acute, and so on. Tactile learners could benefit from “Shaving Equations” where they are solving equations by “writing” in shaving cream. There are so many other really fun ideas on this site that everyone should check out if they get the chance: https://www.scholastic.com/teachers/articles/teaching-content/15-math-games-15-minutes-or-less/

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It concerns me that students might be held back in their math education and even held over to repeat a grade based on slow uptake of basic number facts. As Garnett says, some students will be slow to memorize facts but will not otherwise struggle in understanding math. Holding them back over this would be a huge disservice when we can simply accommodate their needs and continue to expand their conceptual understanding. I love Garnett's suggestion about facts charts and how students will eventually memorize more and more facts by using their charts repeatedly.

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By Tori Grundtisch

Since many students have a strong informal conceptual foundation of mathematics, they struggle with assimilating the new language of math and formal operations into their existing schema. We must bridge the informal math knowledge to formal math language used in school.

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By Tori Grundtisch

Teachers should not put a huge emphasis on computational accuracy and remediating computation, or students will think of math as getting the right answers. Also, students should not be limited or help back because of accuracy problems or if they don't know their math facts. These students may benefit from working in partnerships where they can develop self-monitoring skills, verbalize their reasoning, supply proof to answered problems, and benefit from hearing various ways problems can be translated. Kate Garnett believes emphasizes the importance of verbalization in learning, so enabling students to verbalize math examples and procedures(before, during, after) is one way to help students with math learning disabilities.

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The article discusses that many curricula offer methods to help master basic arithmetic facts, however, it is assumed that these students have a solid foundation of basic number facts.  The article gives suggestions such as creating interactive practice in the form of a game. One activity that came to mind was creating an addition Hopscotch mat, whereas students moved from one space to another they would need to solve the addition  problem.  Below is an example of what the teacher can make for their students.

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By: Perry Moskowitz
I agree with what my peers have already stated. I think that students should be placed in a math class based on their ability and not their age. If a second-grade student is learning fourth grade math that’s what they should stick with. If a fourth grader is struggling with math they should be put into a different math group, this way all the students within that classroom are learning at a relatively similar speed. I think that math needs to be taught in a specific route, and the way we engage our students can include various math games, fieldtrips to get real experience with money, we need to introduce these new topics while not scaring the students.

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By Tori Grundtisch

I found it interesting that students who struggle with visual-spatial aspects of math can be perceived as having an emotional problem or math phobia because they often have strong verbal skills and are very bright. Therefore, teachers may not believe they have a true impairment and their needs are overlooked--a perfect example of how “few children are provided substantive assessment and remediation of their arithmetic difficulties.” Math deficits deserve equivalent attention as reading deficits. These students benefit from consistent, repeated, descriptive verbalizations as well as using concrete materials as they verbalize their understanding. Since they cannot form a mental representation, they must construct a strong verbal model for quantities and their relationships. Accordingly, a strong understanding of the language of mathematics is essential.

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What I learned from the article that I found intriguing was the lack of discussion for arithmetic learning problems. We focus heavily on students reading disabilities, yet I never thought about a student having math learning difficulties, which proves the article’s point. Part of the problem is that we don’t discuss it, so we don’t realize that it is something that affects our students. By having these discussions we can help parents understand that math difficulties can be common, and hope for more research to provide support for those students. I included this photo which brings awareness to October being Learning Disabilities Awareness Month, and that Dyscalculia is included.

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Garnett talks deeply about engaging with concrete materials. She emphasized that the concrete resources do not teach math by themselves, we need to give the guidance necessary in order to make the best use of the concrete materials in our mathematical practices. Having tangible items to promote mathematical development, gives students things that they can feel, touch, and take ownership of.
I also agree with many of my peers, as they add that students should be placed in math groups based on the level of their understandings. I agree with what Garnett discussed about how there is an extreme focus on reading disabilities, and we fell into this myth that it is simply okay to be rotten at math. We need to get out of the mindset that math is scary and place students in groups to go about this learning process in general. Students will begin to admire the process if they are given the tools and guidance to do so.

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While reading this article by Garnett, I was frustrated as she went into detail about how students are not being provided with substantive assessment and remediation of their arithmetic difficulties. Too often we focus on difficulties in reading, which also falls under the categorization of a Learning Disability. Garnett states, "approximately 6% of school-age children have significant math deficits and among students classified as learning disabled, arithmetic difficulties are as pervasive as reading problems". This is a problem, as it is detrimental to our students as they progress through their academic experience and into the 'real world'. We need to start having the conversation with our students' parents, fellow faculty, and peers..that mathematical difficulties exist and they need to be addressed in the academic setting. Math is its own language and this made me recall Randy Palisoc's video and how he discussed the myth that "some are just hardwired for math".

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When a student is struggling with the language of math, I really liked Kate Garnett’s idea to have that student “play teacher” - to explain aloud what they are doing as they do it. Garnett describes how having a child “play teacher” when doing math, can be fun for all ages and levels, while also helping them to better understand the math that they are doing. I feel like I even sometimes do this myself when I am doing my own school work. If I am confused, and not grasping something right away, I pretend that I have to teach the concept to someone else, and pick it apart in a way that I can easier understand. It is definitely true that you learn something better when you are doing and explaining something for yourself as opposed to just watching how to do something then having to silently do it on your own.

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A structured curriculum does not leave much room for math exploration and play. All students learn differently and math can be a difficult subject for some. With a not so structured curriculum there is more room for differentiation, partnering, discussions, and math play. These are important aspects of math and should be implemented into the curriculum. This gives students the chance to develop math skills through different activities.

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The article talks about how learning disabled students have difficulty memorizing basic math facts. Students can use charts and different tools to assist them during math instruction and activities. Although basic math facts might be difficult for some students, they can still proceed with different styles of math problems. It is important to allow students to progress with their math even if math facts are not memorized.

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I think it must be incredibly frustrating to have a specific math related learning disability and to have it overlooked because more emphasis and attention is put on reading disabilities, as explained in the Garnett article. When following a structured math curriculum a student with a learning disability can more easily fall behind when the teacher is focused on staying on track with what needs to be taught. If one skill such as memorizing basic math facts is not mastered, then that student can have even more trouble when the problems become more complex, therefore making it even more difficult to get back on track.

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The language of Math:

I really like this idea of having students, “play teacher,” while doing math. In my opinion, it is a refreshing perspective for math instruction. Personally, when I study I utilize this concept during my study sessions to help reinforce the material. Also, this is a great way for students with LD to reinforce academic language and exchange ideas.

Some great tips per the article include: Read aloud the problem and the answer, listen to myself and ask, “Does this make sense?” These are great tips because it gives students the opportunity to do some self-reflection based on their work.

The written symbol system and concrete materials:

Student’s background knowledge and prior knowledge can deeply affect their outlook and comprehension of mathematics. For example, a student with informal mathematical comprehension this can help with their understanding of the materials (per article)

I  agree that, “Students need repeated exposure & experience of any varieties of concrete materials to make these connections strong and stable.” This will help students understand the material through repeated exposure.

In my opinion, having students work in pairs and exchange ideas is a collaborative effort that increases their enrichment with the material.

The author does a great job in specifying that concrete materials do not just work by themselves, they go hand in hand with the concepts taught in class. These materials can vary, and should be utilized heavily with students in the elementary years.

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One challenge I considered is the push towards the abstract. Students are given concrete materials at first but are encouraged to move away from them very quickly. A student who relies on the support of concrete representations as opposed to moving to pictorial or number sentences is often considered behind or in need of remediation. The need for manipulatives and informal  representation gets associated with lower level understanding, so these methods are not encouraged. Students with disabilities especially could be facing additional hurdles by pushing them to use a more 'sophisticated' strategy. The article describes this by saying that even pictures are technically abstract, and " if introduced too early, they easily confuse the delicate connections being formed" about essential topics.

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As mentioned in the article, some suggestions include using interactive and intensive practices such as games to teach mastery of basic arithmetic facts. Breaking facts into groups and allowing students to self-monitor was another suggestion. In the classroom teachers and break facts into groups and use these groups in a game to help with attentiveness. Math is a subject that at first glance is very difficult to understand for some students even more so if they have a disability. By using games as a guide for teaching, students can learn though having fun which will make the process easier for them.

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With a structured curriculum, students are expected to arrive at a specific point at a specific time. However, all students learn at different paces especially if they have a learning disability. These students may not progress at the same time and may need extra help each step of the way. Even then, its possible for them to have difficulties catching up. They might also excel at a different part of the curriculum but not the one currently taught. Something interesting mentioned in the article is that some students with difficulties in remedial math can join honor classes in higher math. This is something that may not happen if students are denied the opportunity in lower grades or are held back which can more harmful than helpful.

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Implications For Play!

When considering our LD students, there may be implications for play due to visual-spatial aspects of Mathematics. For example, Garnett described how LD students can have difficulty with pictorial representations and confused arrangements of numerals and signs on paper. This can make it difficult for students to engage in math-related games implemented in the classroom. Personally, this is something that I would not have considered prior to reading this article. Moreover, there are plenty of games that could be confusing for these students.

I found this wonderful website that incorporated various activities for LD students:https://www.brighthubeducation.com/special-ed-learning-disorders/80969-game-ideas-for-students-with-dyslexia/

This website includes activities such as: Snakes & Ladders, Addition & Subtraction on Steps, Musical Numbers, The Apple Tree Game, and The Classroom Game Board. These are all wonderful ways to incorporate in the classroom that will benefit diverse student populations. My personal favorite is the Addition & Subtraction On Steps because it motivates students to be physically active, while engaging in Math.

Lastly, as Garnet emphasized in her article, “It is important to recognize that average, bright, and even very bright youngsters can have the severe visual-spatial organization deficits that make developing simple math concepts extremely difficult.” This is an important point here because it highlights the key idea that teachers cannot have false expectations of their students. This is unfair for the student and the educator for having expectations that the student cannot possibly meet due to their limitations.

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Games, Dyslexia and Math:

Children with dyslexia often struggle with math, especially number forms and number concepts. They tend to find math difficult, even frustrating. Games are a great way to help children practice math skills and have fun at the same time. They also tend to require the use of multiple senses and thus promote better learning and retention. Here are a few games you can use in your classroom. The best part about them is that you can make them yourself. So have fun making your own math games!

Ideas:
Snakes and Ladders for Dyslexia:
This game is based on the regular snakes and ladders, except that it has fewer numbers. Make a board with numbers from 1 to 25, or 1 to 50 depending on the numbers the child is familiar with. Use large squares, and fewer snakes and ladders. Make sure the snakes and ladders are different from the colors used for writing the numbers. Use markers on thick card to make this board, and laminate it. Pick up some dice and get ready to play.
Addition and Subtraction on Steps:
Here is a fun game that you can play with one to three children at a time. On a staircase write numbers from 1 to 10 starting from the first step and ending with the last. Make a spinner with numbers +1, +2, +3, +4 , -1, -2, -3, -4 Each child gets a turn. In the beginning of the game everyone stands at 5. Then they spin the spinner. If they get +2, they have to go to 5+2, that is seven. Similarly if they get -3, they have to go to 5-3, that is 2. If a child gets a number that goes below 1 or above 10, they are out of the game. The child who stays in the game the longest, wins.
Musical Numbers:
Draw a large circle on the floor. When the music is playing, the children run around the circle. When the music stops, you show the children a flashcard with a number written on it. The children need to get into groups of that number. Groups that are having the wrong number of children are out of the game.
The Apple Tree Game:
For this game, make a huge apple tree on the board. Also make a lot of small apples or cut out red circles. a dice for this game. Every child gets a turn to roll the dice. After that, they have to take the number of apples shown on the dice, and put them of the tree ( you can use tape to stick the apples). In this way you go around till everyone gets a turn to put apples on the tree.
The Classroom Game Board:
This game is a variation of usual game boards. Glue A-4 size papers on the classroom floor to make a path. Color a few of the papers red, and a few green and leave most of them white. All the kids stand at one end of the classroom. Each child throws the dice and jumps from one paper to another, according to the number on the dice. If they land on a red they have to sing a song, and if green, they have to say a rhyme. In this manner, every child gets a turn.

These are just a few ideas to get you started. Build on them, modify them, and create your own games that work for you in your classroom.

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Math Games For Students with Dyslexia or Learning Disabilities: Teach Math Through Play

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Children with dyslexia often struggle with math, especially number forms and number concepts. They tend to find math difficult, even frustrating. Games are a great way to help children practice math skills and have fun at the same time. They also tend to require the use of multiple senses and thus promote better learning and retention.

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Making the Abstract Concrete by Alexandra Suarez 

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Making the Abstract Concrete by Alexandra Suarez 

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Something many students struggle with in terms of math is connecting with concepts that have been taught in an abstract fashion. This is especially pertinent for students who have a math disability. By using manipulatives, and giving students different physical materials to explore math concepts with, students are more likely to grasp what's being taught. Allowing students to learn through play- at any age- is incredibly beneficial; it can aid in many of the areas Kate Garnett mentions such as acquiring basic number facts, and computing different equations. Many students already feel that play is fun, and connecting the two, can make them find the joy in math too!

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By Jessica Batson
Math as a language can be difficult for students with learning disabilities.  Math vocabulary words often times do not have root words that can help define the vocabulary. A great way to encourage math as a language in the classroom is by modeling it for students. When explaining how to solve a problem, use terms such as quotient and product. Follow up with defining the word each time you use it as well.

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By Jessica Batson
Math is often seen as a "serious" subject that requires repeated practice of skills and strategies by pencil to paper. Often times, giving students a set of manipulatives and encouraging them to "explore" them can lead to math development on it's own. In college, a professor of math I had gave us two full weeks to play around with fraction strips and counting cubes. As students, we were able to make concrete number connections and models based on problems we developed on our own. Although we were "playing", we were still learning.

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A tension that arises for me is the way students are meant to be evaluated according to the
standards of different curriculum. Teachers can all agree to value individual student strengths and support students with disabilities, but then submit rubrics that tell a different story. As teachers we want to make sure students are willing to make mistakes and aren't focused on the right answer, but mastery of the curriculum might require that very thing. I think a lot of confusion occurs for everyone when the curriculum asks for evidence of proficiency in ways that are at odds with what teachers value. For example, a teacher may need evidence that a student can explain there work. During class they accept explaining in the form of writing, drawing, or thinking out loud. But at the end of a unit they must turn in a summative assessment for grade wide data collection, which only accepts student explanations in full sentences as proof of understanding.

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Many curriculums incorporate the use of calculators and how to properly use them to figure out mathematical facts. Although I fully support the proper use of calculators for those students who struggle in math, I also feel that students should not always rely on a calculator as a “crutch.” Having the knowledge of the skills is likewise just as important, if not more important. Therefore, I like the suggestion of students having a mini pocket chart to figure out facts- that way, as they are figuring out the answer, they are also working on the skills needed as well as working towards memorization of the answers due to the constant repetition and solving of the equation.

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Some students who have difficulty with computational accuracy during their elementary years are often placed into honors classes in higher math as they get older. If children consistently remain in low level secondary math classes, they risk having access to higher level math would they could eventually succeed. This is due to their math level being determined primarily on lower level skills where often careless mistakes and inconsistent computational occur.

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I think the problem with have a structured curriculum is that it doesn't leave room for the magic to happen. When the students or you are feeling inspired by the way the lesson is going and you want to take the lesson in a different direction, one that you think they will gain more from based off the way they are reacting to the current lesson, but then you remember that this very structured lesson doesn't allow for you to veer off course. I personally don't like the idea of being "stuck" in one specific lane. I like the idea of leaving room in the curriculum or lessons for spontaneity or classroom inspiration to happen.

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One of the challenges that can arise is the language used in math. LD students can become hindered by the language used in math problems which then leads to confusion on multiple levels for the student which ultimately means they are having a harder time understanding the lesson than perhaps other students.

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I think using a structured curriculum puts a limitation on different ideas that could be used within the classroom. Every student learns different and using structured curriculum assumes that all students are the same. I also believes it stops students from truly understanding what math is. In addition, it makes it harder for students to make a connection between math outside the classroom and math inside the classroom.

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Using concrete teaching materials as Kate Garnett mentioned in the article. With concrete materials, children are able to see the numbers "visually". Another possibility is creating stations that address the different learning needs of students. One station could be for students who need concrete materials, while another station has visual concepts for those who rely on it, and a station that has cards. Giving students these different options allows them to partake in math rather than just listening the teacher go on about math facts.

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I think Garnett's notes on the social myth that being "bad at math" is acceptable is poignant and needs to be addressed by classroom teachers. Many teachers themselves may be subject or believe this "myth" about their own math abilities. In fact, she points out, that math is innate, it's just often the connections that learners don't make of their own abilities and knowledge and what is formally taught in the classroom. Encouraging a growth mindset, and squashing the idea that "some people are just good at math, and other's are not" is crucial to educating children in math.

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One major challenge in mathematics is that many students continuously have trouble memorizing the four basic operations. Despite adequate understanding of how the four operations work, many students struggle to memorize basic math problems as efficiently as they are expected to,

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By: Katie Donohue
Having previously taken over a maternity leave position and teaching math (and the other subjects) to a group of second grade English language learners, I was really able to experience what language barriers can do to success in math if they are not appropriately addressed and managed. In order to help my students who felt as though they had no foundational math skills to work with because of their different backgrounds, I needed to begin exercising culturally responsive teaching. One of the ideas mentioned in Garnett’s article that I needed to do regularly was to practice chunking while speaking about math problems. Slowing down the delivery of the information that was imperative if I wanted my students to not feel overwhelmed before they had even started attempting to solve the problems! As Garnett also mentions, many students have a ton of informal math knowledge, and cannot make the connection to the formal school-math on their own, so we as teachers need to be the ones to make those connections for them. I just want to add that partner shares really helped my students, because they felt safer possibly stumbling over their words in a very small setting than they did answering group questions.

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I think this way can be controversial because it teaches students what to think, not how to think. And this method doesn’t allow students to strengthen their critical thinking skills. I also believe that establishing a specific, structured method of mathematics instruction, doesn’t give any leeway for individualized learning. All students learn differently, including SWD, so this needs to be considered. For example, having 2, 15-minute instruction periods rather than 1, 30-minute instruction period might be a hindrance to those who could benefit from having one focused period. On the other hand, it could be good to break it up into two segments. It’s hard to say--which is exactly why it isn’t good to have a set method.

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Many students are visual, kinesthetic, and tactile learners. So giving them objects to play and sort through can be beneficial for them; it will allow students to make their own connections about math through play. Math can be made fun by learning with tangram shapes (a method that Professor Gyles taught us this past Spring 2020 semester). Additionally, students can use candy or toys in order to develop intrinsic and extrinsic motivation. The candy will motivate them internally, but also externally to improve on their math skills, and show the teacher that they are enjoying learning math and doing well at the same time.

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RESPONSE TO JULIANNE MOORE - BY TAYLOR BRENNAN 

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RESPONSE TO JULIANNE MOORE - BY TAYLOR BRENNAN 

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Julianne, I loved your response for this column. Mainly because, I tried this in my own classroom yesterday with a student that struggles with mathematics and confidence. He had the chance to explain the problem and "play teacher' himself and the happiness and engagement that he had was truly amazing. I also have talked exam study guides out in the way I pretended to be the teacher of many topics, and I feel as though I have had better retainment of those topics, in multiple content areas. Thank you so much for your response.

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RESPONSE TO TAYLOR NELSON-BY TAYLOR BRENNAN

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RESPONSE TO TAYLOR NELSON-BY TAYLOR BRENNAN

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Hi Taylor, I also found this to be a challenge. Many of our students who have trouble with reading, also have trouble with math and we often pay too much attention on reading because sometimes educators think of math to be a daunting subject. We are often put in positions to emphasize more time on reading than writing as well, this very much confused me during my observation hours during the fall and spring semester. I am lucky to be in a school right now where mathematic struggles are addressed with individualized plans. Thank you for sharing!

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I am honestly not a fan of structured curriculums. I believe that with these curriculums, students feel pressured and overwhelmed with having to master multiple curriculums. This can have a negative effect on how well they are suppose to do when being assessed whether its through state test or weekly school test/quizzes.

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Kate Gernett mentions how "Students may respond to repeated failure with withdrawal of effort, lowered self-esteem, and avoidance behaviors." With that said, if they are struggling in math it may result in them mentally withdrawing from the subject completely. I agree with many of my peers that placing students in math classes based on their mathematic ability could be beneficial. This can help raise a student's confidence about their math abilities which can also lead to possible progression.

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Hi Perry,

I think that's a succinct way to put it - that math is a second, or additional language that needs to be taught. I think it highlights the idea that we need to learn this language, and the idea that some will be absorbed if we're in a language-rich environment (like putting math terms on a word wall). If we use our "language arts" tactics with math we might be able to help children access math better. Maybe they're not so different after all...

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Thank you for sharing addition hopscotch. I think this is a great way to provide access to children, especially those who are kinesthetic leaners. If someone was differently abled in terms of mobility, they could also engage but rolling or walking over the squares. I can see this being a very helpful activity that connects math with fun and play.

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Response to Katie Donohue by Chelsea Lopez 

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Response to Katie Donohue by Chelsea Lopez 

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I was really interested in your discussion about teaching in multiple locations. I think about how we have students sit in the same desk for hours and rarely incorporate fun activities out of their seats. I like the idea of Simon Says and making a fun childhood game a way to teach a math lesson.

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Response to Kaitlin Bell by Chelsea Lopez 

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Response to Kaitlin Bell by Chelsea Lopez 

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You made some really great points in your post, one was that students often find themselves in the position where they feel that the only way to pass a test is to memorize the formulas. Yet for students who have difficultly with memorization, they are at a clear disadvantage. I think it is also important that we interconnect our lessons and instead of focusing on addition for one week and then focus on subtraction the next, we blend the two to help our students have a solid foundation.

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Jessica,

I love your idea! I think it would be a great idea for schools to create math groups for students who are at similar levels. I think I really have seen only schools teach math to an entire class instead of students learning in smaller groups. It is important for students to fully understand math concepts before moving on to learning harder ones. I think your idea is great and a lot of students would benefit from this being implemented in schools!

Taylor Nelson

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Anna,

I agree with you that many students struggle to learn and memorize basic formulas. I know a lot of teachers would disagree with this statement, but I think that students should be given formulas instead of having to memorize them. I do not see the point in memorizing formulas. If the student’s know how to use them to solve the problem then that should be good enough! A lot of students struggle with this and put emphasis on memorizing formulas and then really struggle with figuring out how to even use them! Memorization is hard enough for elementary age students.

Taylor Nelson

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By:
Perry Moskowitz

I am also not a fan of structured curriculums.I agree with everything that you are saying, that this structure makes both students and teachers stressed and under pressure to meet these standards that are created by the state.
Thank you for sharing!

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By:
Perry Moskowitz

Chelsea I loved that idea you shared when it comes to math games and hopscotch. I can totally picture my kids engaging in this game, and it helps with physical movement for those who need that kinesthetic learning. There can be many adaptations to this game within the classroom to target the different students needs. Nice job! I enjoyed reading over your post.

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By: Risa Scharf
I agree with everything you said! Understanding the language of math is crucial, as it has an effect on everyday life. I think that is why word problem are difficult, but why they are necessary. Word problems come into direct contact with the math language AND it involved integrating and applying concepts to real life situations. I try to present at least one word problem to my students on a daily. Thanks!

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By: Risa Scharf
I think kids being group by ability and by grade level is important too! As a result of COVID, our groups this year are more diverse in ability, and although that evokes interesting discussion and one can differentiate, it is definitely more challenging on the teacher and sometimes the kids. I am still working on creating a good balance between my students' ability level.

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Hi Miaochang Lin!
Thank you for your response, I think that as teachers we definitely do need to realize that word problems can be tricky especially for students who have dyslexia or other learning based disorders. I think we need to put vocab in that they see over and over again to help them understand and simplify these word problems. We also need to teach them what they should be focusing on in the problem.

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Tori Grundtisch

Risa, I love the idea of teaching math based on a language familiar to students and building from their current understanding. Their informal understanding of mathematics can be developed through play, which can then be refined into a more formal understanding/formal language as their mathematical understanding progresses. Connecting math to real life experiences makes mathematics more accessible and meaningful, and providing multiple representations such as concrete visuals allows students to build their conceptual understanding. I like how yow slowly build up to fact families, bridging concrete to abstract thinking.

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By: Tori Grundtisch

Julianne, allowing students to “play teacher” is a great idea! Students love when roles are reversed and when they have a chance to engage in different responsibilities, or anytime they can “assist” a teacher. I have noticed that students love when I ask them to help me explain something to their peers, or when given the opportunity to share a strategy on the whiteboard in front of the class. Allowing students to play teacher empowers them, builds confidence, and solidifies understanding. It also provides a unique opportunity to informally assess student’s thinking of mathematics and clarify any misunderstandings. Explaining or teaching something to someone else requires a solid understanding of the material, can help identify any gaps in understanding or further enhance one’s own understanding.  Some students may also benefit from learning from their peers, so the “teacher” and learner both benefit. I think this is a great possibility. Thanks for sharing.

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Response to Katie Donohue - By Julianne Moore

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Response to Katie Donohue - By Julianne Moore

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Hi Katie - Great post about the challenges of providing math instruction to ELLs. You provided so many great ideas that I hope to one day use in my future classroom. I like how you mentioned the idea of culturally responsive teaching. I believe that that pedagogy is so important to implement in all subjects and classrooms. I also especially loved your ideas about doing partner shares. I could see how it could be beneficial to pair an ELL with a native speaker of English, and maybe that student can provide a more unique way of helping the ELL and making the information click for them in a way that you as the teacher haven't thought of. Thank you for sharing!

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Response to Annmarie Scalcedo by Julianne Moore

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Response to Annmarie Scalcedo by Julianne Moore

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Hi Annmarie - I loved your post and your ideas that go against having a structured curriculum! I completely agree. In my opinion, that's definitely when students learn best - when you can offer them a unique, creative way to interact with a topic/information; When it's something that they can appreciate and relate to, not something that is simply taken directly from a textbook. Thank you for sharing!

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Hi Jessica!

I'm also not a fan of a structured curriculum. State standards imply that learning is a "one-size-fits-all" experience which isn't inclusive for students with disabilities. I also feel like standards focus too much on skill, rather than content (e.g. teaching students to memorize complex algorithms rather than teach them why we would use the algorithm).

Thanks!
Anna

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Hi Shuangli,

I totally agree that children can really benefit from math games. I also think that the earlier you expose a child to mathematics play, the more likely they are to succeed in math. This can be as simple a sorting activities, building blocks, or playing with counters.

Thank you!
Anna

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Many subjects leave room for creativity. Whether it is literacy, where the students could act out scenes, use props for retells, and/or have reading celebrations or science where they are doing hands-on experiments and/or having science fairs, there are always ways to incorporate “fun“ into the task. But for math, it appears as if it is a subject that is just about memorizing rules and applying it to the equations.

I believe by incorporating “fun“ into math, it would make the students look more forward to the subject rather than dreading the redundancy. And most of the time, if the students like the subject, they will do well i it- and visa-versa. So it is up to us as teachers to really engage our students!

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A structured curriculum can be very difficult when applying to students with special needs, especially in math. In literacy, there are sometimes ways around adapting the curriculum to fit the student. But when it comes to math, it is more of a concrete curriculum with not much room for adaptation. And as educators, we know that there is an a “one-size-fits-all “approach. Being able to have more flexibility with a curriculum allows for more students to benefit from differentiated learning.

I can resonate with you when you mentioned, "Being able to have more flexibility with a curriculum allows for more students to benefit from differentiated learning." I believe this to be true LeeRose. I truly believe that at this point they just want us Speial Education teachers to use the structured curriculum as best as we can with our students. They need to at least help us out with best practices resources or platforms to help us with our students. -Paola German

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Hi Taylor,

I agree with you that Math consists of various things for our learners to understand. This can be difficult, if the teaching methods are not effective & students are left to figure things out on their own. Or they are frustrated and showcase behaviors because they are not receiving clear communication regarding topics discussed in class.  Memorizing will work for some students but this does not mean it is an effective way to get through to our students. We have to be able to have students activate those brain muscles and utilize prior/background knowledge and link and make connections with new information.
Jennie Haque

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Hi Risa! I loved that you incorporated your personal perspective & that you demonstrated scaffolds and visual aids that you are utilizing in your classroom. My Co-teacher also utilizes math cubes (counters) and visual aids similar to yours as we are teaching our first graders addition based off on word story problems. And, as you can imagine, story problems can be difficult for young learners because of the excessive information. They have to be able to filter out the information they need to complete the task.

Jennie Haque

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By Mia Avramescu: I agree that there is so much opportunity to use math games to reinforce learning! In my general ed math class at Hunter we learned so many different games that I hope to incorporate into my classroom soon. Also, I am not always a fan of computer game ed tech programs -- I don't think they are often the best way to get at conceptual understanding, BUT, they can be a great alternative to boring worksheets for developing automaticity with math facts!

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By Mia Avramescu: I very much agree with your point that students who have IEPs may often be left behind by a structured curriculum. It may simply not move at their pace. It is so important to adapt so that we are actually meeting the needs of students, not just sticking to what the book says comes next. In fact, that may mean we are moving on to something new right at the moment that our students with IEPs are about to really grasp what we have been working on for days or weeks, and without the extra reinforcement they need, they might actually lose all of that learning.

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This rings very true to me! Equity is an essential goal, but it can be easy to have this idealized view of what it looks like in the classroom. Sometimes the best ideas are messy, and it can be hard to allow that (especially if administration is watching). Students working with all different materials with highly differentiated look does not always appear harmonious, but that is fine if student learning can be proven.

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You both make interesting points about students benefiting smaller groups with students at their level. At first I wanted to protest the idea entirely. This is because I have seen in the past that it can lead to struggling students not getting exposed to the ideas of their peers or to being given lower quality instruction because they are in a "low" group. I was very wary of it turning into the 'tracking' that causes harm to students. However, I admit that you both are correct in saying that small groups are important. Provided that the groups are flexible, students can definitely benefit from being instructed with peers at similar levels. If it is not the only way math instruction is received, these groups could be one of several modes of instruction in that classroom that support students.

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Response to Anna Shepard by Katie Donohue

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Response to Anna Shepard by Katie Donohue

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Hi Anna,
I absolutely agree with you in that self-confidence and perception of the possibility of success in a math class will be negatively altered by consistent failure in the subject. No matter how hard we try, as teachers, to stop our students from comparing themselves to one another, it seems as though it's part of human nature to do that. Recognizing that you're repeatedly the only one who isn't raising your hand to respond or who isn't getting positive feedback can be detrimental to the way that students perceive themselves so it may be better to put them in groups of abilities that are closer to their own so they can experience the feeling of success.

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Response to Charlene McKenzie by Katie Donohue

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Response to Charlene McKenzie by Katie Donohue

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Hi Charlene!
I completely agree with you in that having a structured curriculum means that for the most part we are operating under the assumption that students will be able to access the content at a level that is pretty much the same, which is unfair to expect. Students come from so many different backgrounds and bring so many different pieces of information to the classroom so we cannot assume that they are going to be able to make connections at the same rate or with the same supports. Thanks for your share, it was interesting to read!

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Miaochang, I agree that sometimes the language of math can confuse students. Most specifically, math vocabulary. If students do not know the meaning and definitions of vocabulary words, solving a word problem can be impossible. We can teach vocabulary in the classroom by modeling the words in our daily lessons. Reviewing the vocabulary morning with each lesson can also be helpful.

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In a math classroom, there can be a large gap between student learning and understanding. Some students may still have difficulty memorizing their math facts while others are successfully completing higher level math problems. In my own classroom, I try to differentiate as best I can based on these levels. Typically, students will receive task cards based on their abilities and what they need the most help with. Since our system doesn't allow for students to be grouped on ability rather than grade, we have to try out best to properly educate those students.

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Response to Miaochang Lin:

Thank you for your response!

I think that vocabulary is definitely a struggle with some students. And if there are terms that are unclear, this can carry over into future lessons and lead to more issues. So I think one solution would be to supply students with a mathematics vocabulary glossary for each new lesson. That way they can refer back to it at any time and not fall behind.

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Response to Miaochang Lin:
Thank you for sharing!
I think that vocabulary is definitely a struggle with some students. And if there are terms that are unclear, this can carry over into future lessons and lead to more issues. So I think one solution would be to supply students with a mathematics vocabulary glossary for each new lesson. That way they can refer back to it at any time and not fall behind.

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Response to Risa Scharf:

Thanks for sharing, Risa!

Repetition and consistency are so important. I think that practicing will help with students’ executive function, and ultimately develop automaticity. Furthermore, I agree that building upon old lessons and weaving them into current and future lessons is the key. Then students will have the opportunity to recognize what they already know, and relate it to the present lesson by making connections and building on them.

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I agree, Jessica! I know this may be much harder in a public school, but I think about the school I currently work in which is a small, private school for individuals with special needs and we do this! We cater the entire curriculum based on the students in each of our math groups and the head teacher and the eduction supervisor talk and think about exactly where the students in the math class are and what is realistic for them at this moment but also across the school year.

-Annmarie Salcedo

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I think nothing helps motivate a student to learn more than when they are excited, invested and interested in what they are learning. And so the best way to do that is to bridge their interest in the lesson and math games is a perfect way to do that!

-Annmarie Salcedo

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Hi Gina,
I agree with your statement about structured math teaching students how and not the what. With this type of instruction, students are just learning the standards because they have to. I aslo like your suggestion on breaking down the math into two time periods because some students will need that extra time. This methodcan be controversial especially when the teacher has to meet the state standards but us unable to meet all of her students needs.

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Charlene Mckenzie: Response to Chelsea Lopez

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Charlene Mckenzie: Response to Chelsea Lopez

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Hi Chelsea,
I agree with you that we do not have discussions on math disabilties. Before the teacher would have just chalked it up to the student  struggling and needs to spend more time studying. In my undergraduate studies, I heard about a lot of reading disabilities but not really about math until I came to Hunter. Math is a language that teachers need to take into consideration when they are teaching students with math disabilties.

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Structured curriculum does not leave room for exploration and play. When students have opportunities for exploration and play they are able to more easily make connections and grasp math ideas. Structured curriculum does not give students chances to practice strategies in different contexts. A structured curriculum can be used as a supplement for other math curriculums.

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There are many ways students can be introduced to math play. It is important that students are given math play at a young age so that they can be introduced to math ideas. As students get older teachers tend to fade away from having students participate in math play. This creates disengagement in math for students. When teachers provide students with math games students are able to learn from others, practice basic math skills, and enjoy math. Teachers can provide students with short periods of time throughout the day to play math games. Students will look forward to this time and be able to socialize with other students in the class.

Hey Danielle,
One thing that resonated with me from your post was when you states that, "When teachers provide students with math games students are able to learn from others, practice basic math skills, and enjoy math." I agree with you in that play should be included in all grades. Students will be engaged in learning knowing that they will have to put what they learned into a game. One thing is for sure kids do not like losing so they are going to learn the concepts. So I agree with play being at every age. -Paola German

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Alexandra Suarez's Response to "Accepting Chaos." 

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Alexandra Suarez's Response to "Accepting Chaos." 

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I too agree that a successful classroom does not need to be quiet and orderly. In fact, I think a vibrant, bustling classroom, often indicates effective learning and play taking place! It must be within reason of course, but classrooms that are students centered, utilizing multiple modes of learning, and many tangible math tools will be lively and surely won't be calm!

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Alexandra Suarez's Response to "Ownership."

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Alexandra Suarez's Response to "Ownership."

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I so agree with what Taylor said, and I think promoting ownership when it comes to mathematics is essential, for students and teachers alike. Educators must feel a sense of ownership and confidence in the material they are teaching, to effectively foster this sentiment in our students. It is great to use tangible materials to foster understanding and connect to the concrete, and we want to take that one step further and have our students own, and feel secure in, the material they are learning.

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Hi Mia,

This was also a concern I had as I went through the post. I completely agree that holding student back because of how they were slow to memorize facts is a disservice. As mentioned in the article, some students are slow in memorizing fact, but they will have no issues in higher math. Accommodations are always important, and students should get the help they need to succeed. Thank you for sharing.
-Shuangli Lin

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Hi LeeRose,

I love the idea of incorporation fun into math. Math, like all subjects can be more enjoyable and fun for students to learn if they can enjoy the process. Many subjects such as science and ELA have creative elements that make the lesson more engaging. There’s no reason why math can’t be the same. One of my professor said that we shouldn’t teach a lesson we’re not excited about. If we as teachers don’t feel engage teaching the lesson, then students will reflect it. Thank you so much for your response.

- Shuangli Lin

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Using a structured curriculum won't allow the ability to reach potential misunderstanding that students may have. For example, there are so many concepts in math that students might not get or be on the same page as their peers. This means certain "milestones" will not be reached. Every student is different and having a preset scheduled lesson might not target the needs of that one specific child. As an educator you need to be flexible with what concepts are being taught. This may lead to some students not understanding the lesson and may fall behind in class.

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Many students cannot learn by just giving them a problem on the board and saying answer the question. Many children, especially at a young age need to explore why they are learning it. They also need to see the relation on the math with other concepts that are familiar to them. Children understand and learn more when they explore the information and play within it.

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It is sad that math is looked over when it comes to deciding the disability of a student. We pay more attention to English than math. Just because a child doesn't need assistance with English doesn't mean they don't need help in mathematics. The most important thing we can do is to identify the needs of the individual students and provide those necessary supports needed.

I resonate with you when you said, " The most important thing we can do is to identify the needs of the individual students and provide those necessary supports needed." As educators we will face many challenges with our students. The best advice is this what you said, identifying our students needs individually ensures a successful classroom. -Paola German

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One of the greatest challenges I see in my classroom regarding mathematics instruction is that language deficits greatly impair understanding. This happens often with mathematical terminology and most of my students don't have the language yet to explain their reasoning. I also find that most of my students are visual learners, which makes auditory processing of mathematics difficult. I typically use a lot of visuals and manipulatives in my lessons to allow my students to engage with the material in the ways that best suit them. I believe it is also important to give adequate wait time to give students the time they need to process the language.

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As a k-2 teacher, I have a mix of standard and alternate curriculum students. I find that, even for my standard assessment students, the work needs to be differentiated and individualized significantly. Structured curriculums don't provide much support for students with disabilities or ELLs. Therefore, I almost always end up creating all my own materials that are aligned with the curriculum. All of my students have trouble processing the math vocabulary and language, so it makes it very difficult to adhere perfectly to a structured curriculum. Students require differentiation and individualized supports to access structured curriculum materials.

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I think that structured curriculum's can be very problematic especially for our D75 students who are facing other challenges, in addition to learning difficulties. Our students are also in mixed grades with mixed levels of abilities, so it wouldn't benefit anyone to just teach a structured curriculum that did not meet any of their needs. It is always helpful to have a curriculum to base you lessons off of, but it is important to make them your own and adjust based on what you know about your students.

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One of the biggest challenges that I face in my math class is that my students all have such varying levels of math abilities. Especially during remote learning, it becomes harder to reach them all where they are at and adjust units accordingly. One website that is helpful is called Happy Numbers because it makes each student take a diagnostic exam and then places them based on their score. This way they receive some sort of personalized instruction in math based on their areas of strength and weakness.