Math Curriculum in Elementary School
- See also: Math Enrichment for Young Math-Lovers ... More Math Advice
Parent Q&A
Archived Q&A and Reviews
- Stanford EPGY vs Khan Academy for 5th grader
- 2nd grader says she hates math
- 3rd grader has never memorized addition/subtraction
- Encouraging 2nd grader who loves math
- Why are kindergarteners studying patterns?
- Times Tables -- when?
Stanford EPGY vs Khan Academy for 5th grader
Nov 2013
I am looking for some resources to help my moderately gifted 5th grader who is not challenged by the level of math (among other things) in school. She has attended a math circle in the past but it doesn't fit in with our schedule at the moment. Just received a flier from school about Stanford's online EPGY program, which is $115 for 5 months. It seems similar to the Khan Academy online course, which is free, but is hard to tell. Does anyone have experience using these programs? Did they engage your child? The EPGY also has a language arts and writing module but would this be of any use if she is reading at the high school level? Thanks for any insights! 5th grade mom
My daughter, now in eighth grade, has been doing the EPGY on-line math program for about five years now. (She also did the two-week EPGY math summer camp the past two summers.) EPGY is more structured than Khan Academy. There is a test to be accepted into EPGY, and there are tests to advance to the next grade level. My daughter started in EPGY with third-grade math and was able to work and move forward at her own pace so that she's now studying calculus. She's (usually) motivated to sit at the computer and listen to the lessons and do the problems, so it's worked well for her. Because EPGY is systematic and covers the basics, it complements the Berkeley Math Circle's more varied and unusual subject matter. We haven't tried any of the other EPGY subjects. Robin
2nd grader says she hates math
April 2011
My daughter ''hates'' math. She is not bad at it, but regularly complains that it is boring and too easy. I know this is not uncommon for girls but I am so disheartened to see this happening at such a young age, especially as a female computer scientist myself.
I have talked to the principal several times about the issue, and even had her moved into another class to see if that helped. The new teacher seems to have made it only slightly more bearable for her. I should add that she LOVES this teacher, who she also has for science class, so I do not believe there is a personality conflict going on.
She is really an artist at heart with very strong verbal, visual, and creative skills. It has occurred to me that the real problem is that the Saxon math curriculum just doesn't engage her. I believe the curriculum is great in general - my son is excelling in the program - but no one program works for every child, and this is the only curriculum offered at their school.
What can I do to show her that math is fun, that she can feel confident about being good at it, and that it is not a class to dread? Have any of you been where I am and managed to raise a daughter with a positive attitude towards math? Help please
Hi, It's great that you are looking for ways to keep your daughter interested in math! The book Family Math, published by Lawrence Hall of Science has wonderful math games at different levels for families to play with their children. The book is divided into different content areas (number sense, addition/subtraction, multiplication/division, fractions, etc.) with easy to read directions. No special equipment is needed to play the games. The book is available at most libraries, at LHS in their bookstore, and probably, ahem, on the internet. Good luck! Math is wonderful! And, as a teacher/educational therapist, who trained years ago at LHS in their ''EQUALS'' program, I know that it is a gateway subject for many careers, including medicine, engineering and finance! anon
Sign your daughter up for recreational math classes through Lawrence Hall of Science, and pick up some math game books (Marilyn Burns Math For Smarty Pants); or Family Math; also sign her up for architecture or engineering camp (MOCHA has a good one). School math at that age is pretty limited to computation which isn't all that exciting, but mathematics is much larger than that. Fun math games include legos, connects, zoom, Mastermind, Set, Connect Four. Don't let her believe that computation is all of math. math teacher
I'm not sure I understand why your daughter HAS to not hate math. Because you like math? I know plenty of crazed sports fans who have kids who hate sports. That's just the way it goes sometimes. If it's not affecting her grades ... well, I don't think it should matter, or even worry you. Not everyone likes everything. Sounds like she's interested in plenty of other things to make her world go 'round, don't you? -- I hated college English classes, they hated me, and yet I became a professional journalist.
There's a great book called Math For Girls-math is fun and much more interesting in this book. Look it up. Good Luck! Former teacher
As a child in the 1940s, my mother was told that girls were bad at math. She never proceeded much beyond long division. When her daughters were born, she was determined to do the right thing. From the moment we hit kindergarten, she told us repeatedly how good we were at math. As a kid, this freaked me out -- I didn't like math and for the life of me, I couldn't figure out why it was so important to her. Would she love me less when she found out I was lousy at it? I felt anxious in math class, and trying to please her, I worked my tail off trying to be ''good'' at it. I ended up making it through calculus in high school . . . with feelings of resentment toward my mother for making it such a big deal. I had an awesome mom, and this is probably more an example of how it's better not to tell a kid that they're good at something and instead focus on the effort required . . . but my two cents would be to approach it from a different angle and not get too hung up on what she should like. Math Challenged
3rd grader has never memorized addition/subtraction
August 2005
My soon-to-be third grader has never memorized her addition/subtraction tables. Multiplication was introduced last year and she hasn't memorized those tables, either. She counts on her fingers, usually getting correct answers. When I asked her teacher for advice, I was told my daughter is doing fine (so far she's been getting top grades in math) and will memorize math facts sometime on her own since she's bright and memorizes easily. My daughter says memorizing math tables is boring. I donbMarch 1998t think waiting for sometime is going to work.
Can anyone recommend ways to help a child memorize addition/subtraction/ multiplication (and eventually division) tables? I've heard of a device called the Flashmaster (www.flashmaster.com). Has anybody had experience with this? Is it worth buying? I know there's a Korean or Chinese method for using your fingers to quickly calculate but I can't remember how it works. Could that be a better way to help her out since she already uses her fingers? Does anyone know what this way of finger calculating is called and how it works?
There are (free) lessons online that will take you through a step-by-step method of learning the times tables that seemed quite clever to me. Your daughter might have fun working on it on her own. See http://www.multiplication.com/teach.htm. Good luck! Marta
Hi I just read your note on the Berkeley Parents' Network. I am an educator by training with a few minutes to spare; so, I thought I'd drop you a line.
I think you are right to encourage your daughter to memorize her math facts. And, your daughter is also ''right'' that it can be boring. Unfortunately, memorizing things is part of the ''real world.'' She will need to develop the discipline to do it. Memorizing math facts also makes it easier for students to learn more complex math such as measurement and problem-solving.
The Asian finger-counting is called chismbop or chisanbop. It is fun and I could show your family how to do it. It won't replace the need to memorize math facts; but, it is a fun way for kids to check their own work.
I'd recommend decorating some walls with big multiplication charts, organizing a game of ''math baseball,'' playing with concentration style card games with flash cards, etc. There are also free web-based games and customized worksheets on the web
Depending on what interests and motivates your daughter, you could also set up a contest or reward. There's no need to buy fancy toys or tools if you have the time to create activities on your own. If you are pressed for time (like most of us), I recommend LeapFrog's product line. Hope this helps. Debbie
The finger calculation method you're talking about is called chisanbop, it's simple to use, and you can easily find directions on the internet if you do a google search. I think there is a website by someone named Andy Harris that has good directions and photos of how the system works. Liz
Your daughter is right: memorizing math tables is really boring. If she's doing fine, let her go. I had parents who didn't pay any attention to my scholastic achievements at all, and I tended to be an over-achiever. In fact, I skipped into third grade and was utterly terrified of doing multiplication. Eventually, I just learned it by whatever magic seems to happen to young kids who are paying attention. I don't recall doing any intentional memorization except to the degree that I would get frustrated at not knowing what an answer was (plus what they do in the class), and your daughter may end up doing the same thing when the math gets a little more complicated. What's more important is knowing the concepts and how to derive the answers, and knowing that there are tools (such as memorization) that are available if her existing systems don't work.
In my experience, if you let this slide, and your kid is not very self-motivated, then you are limiting your kid's options later on. My kids never had to memorize much in school (Berk. public schools). I guess rote memorization had gone out of style. There was very little emphasis on memorizing the multiplication tables. As a result, when they got to higher math like algebra, they were at a huge disadvantage. Math was very time- consuming and frustrating since they had to either derive ''4 X 6'' by adding, or use a calculator. Long division was impossible. It just took too long, because they didn't have the tables in their heads. Both kids started hating math around that time, hating doing the homework, hated math classes. By high school it was too late to go back and build that foundation that was missed in 3rd grade. Since math was so frustrating they took the minimum requirements, so they didn't have the prerequisites that would have led them on to sciences in college. Who knows if they'd have loved the sciences and wanted to take that path, but in retrospect I wish I had paid more attention so they could have at least had that option. You are wise to be thinking about this!
My 3rd grade teacher had a record that she played every day for months that had little jingles for the multiplication tables. We all sang along. We started at 2 times everything and worked our way through the 9's. When you sing these jingles, it really sticks in your head and just becomes automatic. You can probably find something like this on Amazon.
My stepson had a pretty bumpy elementary school experience, changing schools often etc. So one of the problems that resulted was that he never memorized his basic math - subtraction and addition! this took years for me to realize...
he took a remedial course in the summer after 6th grade and memorized his multiplication...but in the end, i found out it was his addition/subtraction that still holds him back (will be a freshman in high school this year).
Just sharing my experience because the consequences of not memorizing them are huge! all his math is delayed because you use addition/subtraction in most every math problem and it takes him so much longer and he makes so many simple errors.
For her age, i do think counting on fingers is normal so it doesn't sound like you have much to worry about. But take it in steps, if they are learning multiplication in 3rd grade, make sure she's already memorized addition/subtraction. then for 4th grade, work on multiplication tables...the more they learn in math, the more they will need the basic skills and the longer it will take them to learn if they didn't memorize them already.
Given that, if i had a time machine, i'd put her/him in a program like Kumon, which is very simple, organized way to memorize basic math skills, but also does it using timers to get them to do it pretty quickly and get your kid on it regularly. just like chores, even if they don't want to do it (like they'd rather have ice cream than broccoli), it's something they have to do, and is relatively painless if your child is doing fine in school anyway. even something like 15 minutes every day, have them write down one set of addition (have her add all numbers 0-9 for #1...) and keep it going and make it rewarding.
good luck! whatever you do, don't leave it up to the school. i know some teachers often say not to worry because there are kids doing worse than yours, but that is not the standard you should hold your own kid to! math counts
I'm a 52 yo mom of 2 boys, have a great job with a good income and am well educated. I haven't memorized my math facts either!!! I get along fine in life. I have some of them in my head and sometimes use my fingers. My 14 yo son is great at math... My 10 yo is great at math too but hasn't memorized all his math facts yet either. (I'm terrible at math, but it hasn't impeded my life). I think your daughter will memorize over time without the use of programs, flashcards, etc.(and if not...that's partly what fingers are for). Of course helping her with flashcards or games is great, as long as you're not all miserable in the process. Please relax and don't worry. Especially if the teacher thinks she's doing just fine. Kids develop at different rates. Hopefully she will understand the concepts. Good luck. Non mathamatical mom
I grew up during the Schoolhouse Rock things on TV and my brother and I loved them. My mom bought the album of Multiplication Rock and I still know all my times tables because of those songs: Elementary, My Dear, Three is a Magic Number, The Four Legged Zoo...I believe you can get all the schoolhouse rock episodes on video/dvd. I still know the Preamble of the Consitution because of those things! Little Twelvetoes
I couldn't get my son at that age to even understand the concept of multiplication! You are very lucky she understands it enough to count on her fingers! I spent countless hours teaching my son how to ''count by'' on his fingers. But, once he finally got it, we moved on to listening to music CDs that were based on multiplication. You can type in something like ''multiplication CD songs'' at google.com. Every morning we would spend time in the car (they can't get away from it in the car!) on the way to school listening to the songs until he learned the words... and the words were the mult facts. We would dance silly in the car and sing together. Be sure to only play the 2's until she knows it, then the 3's song, etc. This covers the rythym and auditory learning. At night, we would do good old fashioned flash cards. They work! Again, begin at the 2's until she gets them, then 3's, etc. This covers the visual learning. At the same time play games throughout the week that involve mult. My son and I played a game called ''Countdown'' by a company called Cadaco. He loved it! And it's based on mult facts. I still have it if you're interested and nearby. You can also find computer games that involve mult. We used to have a computer game at my daycare that involved ''catching'' the falling answer to a mult problem before it hit the ground. I am sure you can find something like that on the internet. Daily repetition is the key to knowing those facts. That's a proven idea. Good luck and don't give up! Keep at it EVERY DAY and play with her, study with her, praise her and have fun doing it all! lisa
One possibility for learning the facts is any game you already play that uses dice. You can buy dice with 10 faces, or you can tape higher numbers to the faces of the dice you already have. You can also play 21 with cards (the first person to get 21 without going over wins.) There's also Difference War for practicing subtraction (you each take two cards off your pile, find the difference and the one with the smaller difference wins.)
Most of memorizing math facts for kids without learning differences is related to overpractice - practicing often enough so that memorization is automatic. Games make it easier to have that practice. There is a game Equate which is like scrabble but with equations instead of words.
There are a number of tips on memorizing facts on the Math Forum (at Drexel) website. Look at the Elementary Archive. http://mathforum.org/library/drmath/sets/elem_addition.html
Carol
I can Give the ''Making Math Real '' program, based in Berkeley, very highly. It has been very helpful to my math-challenged 4th grader.They have a website:www.makingmathreal.org. It works! hoffmnds
Encouraging 2nd grader who loves math
Oct 2002
My kid loves math and is doing above her grade level. She is in the second grade. How should I support this love, and supplement what she's doing?
I've already talked with the teacher and in-class possibilities seem limited. We play games from the Family Math book, and I know about ATDP. Has anyone done the Lawrence Hall of Science classes? Do math tutors (for encouragement, not remedial) help? I don't want to overcommit her afterschool/weekend time because I think kids should have time to ''be kids'' - but - it's not happening in her school. A common dilemma, it seems.
Thanks for your thoughts (general and specific). Any advice helpful (except for moving out of state, lol!) anon
You might look into Stanford's EPGY courses http://www-epgy.stanford.edu/ for your second-grader. You could also encourage your school to purchase the program. Many schools do (ours won't) and schools pay less than parents for the software. Seems like a legitimate use of GATE funds. Good luck. Eirik
First of all, THANK YOU for taking the initiative to support your daughter's interest in mathematics. As a mathematics teacher, I am sad to report that gender bias in secondary school math and science, while less overt than twenty years ago, is still alive and well in our classrooms. Our only hope rests with parents such as yourself who have the courage NOT to impress upon your daughter that mathematics is not a feminine endeavor and she would be better served reading fiction or learning to knit (both worthwhile tasks in their own rights to be sure). After all, the talking Barbie doll saying Don't you think math is hard? is not that distant a memory. More recently, in the comic strip Mary Worth (I'm not a regular reader but it happened to catch my eye this day), a young girl returns home from school and hugs her mother, stating that she was doing her family living homework. In the next frame, the girl says I like this better than math class to which her mother responds, Me, too. Lest you think me overly paranoid, why not English class or gym or Social Studies????? Mother and daughter agreeing to take a jab at mathematics reflects our collective indifference to how we teach young women generally. Without being overly critical, were I your daughter's teacher I would be thrilled beyond belief that she was asking for more mathematics. Stepping off my soap box, let me then offer a few concrete suggestions. Limit exposure to books espousing the magic of mathematics. Indeed, Harry Potter isn't responsible for the fact that every number of the form xyyx is divisible by 11. The more hows and whys your child learns, the better (and more confident) mathematician she'll become. And, of course, she'll LOVE it even more. Mathematics is all about patterns, and younger children, as we know, can't get enough of patterns. Next time you're at the 7/11 (OOPS! Sorry everything is a math reference!), pick up a few bags of Skittles. Open each bag and count how many of each color you see. Do those numbers differ across bags? What about the total number in each bag? It's a straightforward jump to histograms and simple descriptive statistics (although that may be too advanced for 2nd grade). Then, with your child, of course, use the Skittles to make squares and triangles. For example, the simplest triangle she'll see is with three Skittles, but you can make one with six and then ten (arranged like bowling pins). See if she can find the pattern in the total number of Skittles required to make the next sized triangle. Try making squares. First, you'll need four then nine (like putting a Skittle in each box of a TicTacToe game). Notice any patterns in the totals here? Can you separate your squares into triangles? If so, in what pattern? This exercise can introduce your child to triangular numbers, square numbers, rectangular numbers, pentagonal numbers, on and on?..What's even more beneficial is that your child is all the while reinforcing simple number facts in a way that does NOT involve endless worksheets with forty facts a page. As you introduce your child to the multiplication table (I'm not quite sure how advanced she is), have her take the standard 10 by 10 table and turn it 45 degrees so it looks like a diamond in front of her. Place a pencil covering the numbers 1, 4, 9, 16, 25, etc. (which, by the way, should be a familiar pattern from the Skittles game) and ask whether the pencil could act as a mirror for your table. Without bogging down your daughter with phrases like the commutative property of multiplication, you can help her discover that reversing the order of multiplication does not alter the result. I would be happy to share more but perhaps I should close. She would love the book Math Curse as well. And, above all, DON'T let her NEAR a calculator! Feel free to email me for further advice. Feed her fascination, and she'll be hooked for life. Enjoy! David
Why are kindergarteners studying patterns?
Dec 2001
We have been looking at K classes for our daughter for next year, and we are curious about the patterning projects we've seen displayed on the walls of several K and 1st-grade classrooms. The patterns involve colored strips of construction paper that are woven together, producing checkerboard formations, or sometimes children appear to be transferring a letter pattern (like ABACABA) to a corresponding color pattern (e.g., red,blue,red,yellow,red,blue,red). I have asked a few teachers what pattern work is for, and all we have been told is that it enables the learning of math concepts. Could anyone provide more explanation of pattern work and its use in math learning? We are really curious; neither of us learned math in this way. It seems like an awfully abstract leap for Kindergarteners. Anonymous
Putting objects in order and discovering/creating patterns are basic learning tasks for young children. It helps them learn to compare (by size, quantity or another quality) and to distinguish or make sounds, objects or actions having a regularly occurring sequence. This is basic learning about the world around them which falls into the math category because it has to do with quantifying objects or events. Comparing quantities and discerning repeating patterns are fundamental to simple arithmetic. The ability to order items from smallest quantity to largest quantity (seriation) means a person can count with understanding of the meaning of the numbers (rather than rote recitation of the words, one, two, three...). The fact that children generally enjoy pattern work and spontaneously create patterns during free play is another indication that this is meaningful curriculum. Louise
Patterning is the conceptual precursor to functions, i.e. algebra. By learning and creating patterns of increasing complexity, children learn how to do things like count by threes (or fours, or whatever). Then they learn how to do patterns that have patterns within them -- and they learn to predict what's coming next. Algebraic functions enable us to predict, too, but in the symbolic language of math.
When they're transferring a pattern from one medium (colors) to another (letters), they're making the link between concrete and symbolic thought. Then perhaps the teacher will guide them to translate from the symbolic letters to another patterning medium -- perhaps shapes. So they start to see how symbolic representations can be useful.
One of my favorite patterns is that of Fibonnacci (sp?) numbers -- 1,1,2,3,5,8,13,21,34,55,89, etc. Can you figure out the rule for the pattern? The cool thing is that fibonnacci numbers are ubiquitous in nature -- the number of petals on a flower is always a fibonnacci number. Follow the spiral of a pine cone, and count the notches -- it's a fibonnacci number.
When I taught kindergarten, patterns were my favorite part of the math curriculum. -- Sandy
I volunteer in my daughter's kindergarten class and I'm responsible for doing a math-related activity with a group of 5 children every week. The activities are assigned for me every week, and a lot of them have to do with having the children make and describe patterns, or arrange objects according to various criteria of similarity. I must say that from this (albeit limited) experience I am extremely skeptical about the value of these activities. It's hard to get the children to get interested in them, e.g. you tell them to arrange coloured tiles or buttons into a repeating pattern, but they always want to make them into flowers or swords or animals (which I can see is more interesting and satisfying). And it's not clear how it's going to help them learn about numbers. My daughter hates doing this kind of thing and has never got into it, but she really enjoys doing simple arithmetic problems and learning about numbers. So I guess I am also curious about whether there really is a rationale for this type of activity. I'm not that concerned about it, since we can always teach her arithmetic on the side, and I don't expect every minute of kindergarten to be educationally enriching anyway, but I still do wonder what all this learning about patterns is supposed to do for the kids. Hannah
One type of math that your child will learn in school is working with numbers, and later variables, in which operations with numbers are generalized. The other part of math learning that children are being prepared for is working from patterns to math statements, which is one of the main ways we describe the world. For example, in the early grades, your child will build squares or cubes with side lengths and heights in various sizes. Later, in algebra, your child will write equations representing how the total numbers of squares or cubes changes as the length of a side increases, or they will look at how perimeter and surface area change. In calculus, they will see problems where they are asked to find the minimum use of materials to enclose the maximum area given specified constraints. Students who have had experience building patterns in the early grades will be able to visualize what they are doing when they are solving these types of problems, rather than relying purely on memorization to solve them. Patterning has always been part of the curriculum -- think back to the clapping songs we learned, or the placemats and macaroni covered boxes that we made for presents. The difference now is the greater emphasis on patterns, which probably came about because some kids had enough experience with it from their own play in crafts and using building toys, while other kids (mostly girls) entered abstract math classes with insufficient concrete experiences. So, look for kindergartens where the children are making patterns using a variety of materials, and are talking about their patterns. Carol
I would like to add that working with patterns supports other areas of the curriculum, as well. Language is filled with patterns, and children who learn to look for them are spared from memorizing rules. Reading instruction in the early grades relies a great deal on explicitly teaching children to recognize patterns in written language. For example, children learn that rhyming words generally follow the same spelling pattern. They use this knowledge to read and write new words. Loralee
Times Tables -- when?
March 1998
At what age do kids learn their times tables these days? Or maybe I should ask, at what age should they know them? I know some kids in 5th and 6th grade who have been taught to count on their fingers, and that's where they're still at. I'm shocked, but maybe for no good reason? Carol
Re: Times tables - my son is in the 3rd grade at LeConte Elementary here in Berkeley and he is learning multiplication, although they do not seem to be learning the times tables per se. I distinctly remember learning them myself in the 4th grade. I'm toying with the idea of teaching him the times tables this summer, as a fun thing to do in the car. Chanting the times tables is almost the same as chanting a poem, to me. Dianna
At school my daughter learned the times tables (through ten) in third grade. At the beginning of fourth grade they reviewed the times tables and extended them through 12. (It's possible they began the process during second grade, but I don't remember.) Susan
Our kids were drilled in facts (+,-,x, division) in 4th grade. They had 1 page sheets of each type which they kept testing themselves on to get their time down (and kept graphs of their progress.) Barbara
Regarding learning multiplication tables. Mastery (memorization) in 3rd grade with review in 4th grade. It was a class/home project to learn addition and multiplication math facts in third grade. Kathryn
My son is in the 5th grade and he is not very familiar with the multiplication tables yet although he does know it. He still needs to think a little (and I'm sure do some adding in his head) on it. However, I learned the multiplication tables in Taiwan as a first grader and was definitely able to give the full multiplication table (up to 9's) by the end of 3rd grade. Since I was definitely anywhere among the top of my class then, I know that children are capable of knowing it by start of 4th grade.
I think the educational system here tries to avoid memorization (maybe a little too much in my opinion). I think at some point, the kids just have to use memorization/repetition to memorize things. We try to do alot of math with our son at home. We do try to help him to do some repetition in writing the multiplication tables and continue to review with him. At the same time, we try to let him use it on a daily basis whenever we can such as grocery shopping at the local store, or even when he buys candy with his own money. Diane
Like Diane, I learned my times tables (up to 9's) at age 6. My mom and I just sat down together and chanted them, with a little cheat sheet with nine columns of decreasing length, organized by 1 x _, 2 x _, etc, to 9 x 9. The memorization certainly didn't hurt my later learning of the concepts behind multiplication; in fact they probably helped me see the patterns that times-ing makes, better than I would have otherwise . (I remember little diagrams with squares made out of dots; and also noticing how there were nine 1 x _ facts, eight 2 x _ facts, and later I realized this had something to do with commutativity....) I think it's not a bad thing to have these facts in your head without having to punch them into a calculator; this way you're better able to tell when a typo or whatever has been made and the output is way off in the wrong neighborhood. Not that memorization solves everything... later my father tried to teach me algebra by rote, which is kind of inappropriate. But for the times tables early memorization really does a good job. Joyce
I have so many thoughts about this! My own daughter sounds similar to yours and is now in 7th grade. It has been a multi-year project to keep her open to math in her life. I would like to say there is some magical program that will do it, but in our case, it has been my own work and messaging over many years. Big areas that have helped are...
1. pointing out math in the world and/or when she is using math or thinking mathematically. We are all using math all the time, for all kinds of things (comparing prices at the grocery store, figuring out what time to leave the house to arrive somewhere on time, etc.) Kids learn from school to think of math as some separate activity or mode of cognition. It's not. So just pointing it out and pointing out the ways that she is already using it successfully is really helpful.
2. Play lots of games together. If she's at all open to or interested in board games, there are a ton of them that build mathematical thinking skills. Some favorites for my family have been: Qwirkle, Set, Prime Climb, and Blokus. There are a lot of D&D-ish board games (e.g., Dragonwood) where kids are actually making decisions based on odds/probabilities. Sorry! and Trouble are terrific for practicing basic counting but also optimization. So play lots of games.
3. We give our daughter messages all the time that real math is so much more interesting than school math. In other areas, I would never throw her school/teachers under the bus, but honestly, in this one area, I believe our schools completely fail, and it's more important to me that my daughter stay open to having math in her life later than that she think highly of her school. So I am just really blunt about it. Math is super interesting. School is generally only focusing on one area of mathematics (successful and speedy computation), but there are all kinds of other skills kids will need if they want to move forward in math, including the ability to persist through confusion and difficulty, the ability to think deeply and be patient, a playful openness and a willingness to try things out and make mistakes, the ability to ask good questions and to just look at scenarios and wonder freely. These are all things that real mathematicians need but that our schools don't value at all (except for the rare exceptional teacher here and there).
4. We are opportunistic about diving into math with our kids when it comes up naturally in our lives. When my son was in 1st grade, he wondered if Santa could possibly be real, because how could he get to all the houses in one night? So we sat down with the kids and built some models to try to figure it out (how many kids are there just in the city of Oakland? How long might Santa spend at each house? Side question: how many cookies would Santa have to eat?) It was crazy fun, and the kids were willing to participate because they were keenly interested in the results. I am always on the lookout for opportunities like those and jump on them when they arise.
5. Kids stay open to subjects that they feel good at. If your daughter can have experiences where she gets to experience the thrill of victory, that can be huge. If she is not getting to experience that in school, you may need to provide that for her yourself. Bedtime math is a great, free app. You could look into after-school math circles or clubs. You could even start one - google crazy 8's, a free program offered by the Bedtime Math folks.
Good luck!
Have you thought about an educational therapist or psychologist? They can help with the subject learning and emotional aspects. I have a friend (personal relationship, thus I can't say I've used her services) who is specifically a licensed educational psychologist focused on supporting students in math, please see: https://www.adenayoung.com/.
I'm sorry to hear that math was a casualty of 3rd grade during the pandemic. We had a 3rd grader back when the pandemic started and we were able to introduce a lot of age-appropriate math while baking brownies etc. When we gave up on public school for 4th grade, she was placed into a multi age classroom at a private school where 4th-6th graders were learning 5th or 6th grade math. Kiddo was nervous and I double checked to make sure that we really were assigned a 5th grade textbook correctly. The teachers assured us that many topics are revisited each year. While your child may be a bit confused at times, I can assure you that at least in our case, it wasn't the end of the world. Yes, there were gaps, but hopefully the new teacher or your child will make those known to you.
My kiddo HATED math and I have a graveyard full of broken pencils to show for it! The stress of it just exacerbated the problem. Then we found Ali Mansour at Firecracker Math and everything changed! Ali helped my child develop so much math confidence and an actual appreciation for math! We hired Ali last summer for one weekly private session, and my child, who was a full year behind in math prior to the summer, got 100% caught up and ended up being one of the strongest math students in their class last year. Everytime we had a challenge in math class during the past school year, we did a session with Ali and magically, all the stress and anxiety of not understanding a new math skill would evaporate. If you can get a few sessions with Ali, it could be a gamechanger.
Recreational math— Origami, games like Ken-Ken, Set, Connect 4, Apples to Apples. The LHS bookstore has many books some more directly related to school math, some on broader topics. You could also check the Exploratorium website. School math tends to be very narrow, and often doesn’t include the early learning that prepares children for college math or applications— ie the connections between paper-folding and topology.
Look for fun math games, as lfK suggests. There are a bunch online you can do with regular dice. We used Math Dice, which encourages some creative thinking with math while giving math-facts exercise. Also consider Mancala, an ancient African game. Lawrence Hall of Science (where we discovered Mancala) has a book and gift store with a lot of games that might work for you.
Second, build in rewards. Nothing big, but lots of them. It helps ease the unpleasantness of a distasteful task, and I think retrains the brain such that the task becomes more enjoyable. Playing math games is a way of tying a reward (social interaction, the chance to win, etc.) right into doing the math.
For our daughter I got a bunch of colorful glass beads, all different, from a bead store -- they sell bead odds and ends sometimes by the scoop. She got one or two for doing what we needed, and later could trade them in -- a few for a sparkler, more for a trip for ice cream, etc. I know it sounds mercenary, but it's one of the behavioral-modification things they recommend for kids with ADHD (which she has). If your son barely tolerates a math game, give him a prize for winning. Give him rewards for doing his homework, for getting a better quiz score than he got last week, etc.