《Fred 的生活》（Life of Fred）挺有意思的。不过你可能得把故事读给你儿子听。我大女儿最喜欢的《教学课本》（Teaching Textbooks）有视频辅导。《新加坡数学》（Singapore Math）也不错。还有一些程序你可以……
Life of Fred is pretty entertaining. Though you may need to read the stories to your son. Teaching Textbooks, my older daughter's favorite, has video tutoring. Singapore Math is good, too. There are programs you…
……另一个好玩的游戏是 Tiny Polka Dot——我们自己捣鼓出了超多不同的玩法。https://wordpress.com/posts/bancosparenting.wordpress.com 至于正经书，我们真的很喜欢《Fred 的生活》（Life of Fred）。https://www.rainbowresource.com/category/9813/Life-of-Fred.h...
…Another good game is Tiny Polka Dot - we've come up with so many of our own variations on the games. https://wordpress.com/posts/bancosparenting.wordpress.com In terms of actual books, we really enjoy Life of Fred. https://www.rainbowresource.com/category/9813/Life-of-Fred.h...
为了回答你的问题，我见过提出反证法的学生里年龄最小的是八岁。那个小女孩读过几本关于数学的儿童读物《Fred 的生活》（Life of Fred，http://www.lifeoffredmath.com/），才刚加入我的本地数学班。才上了第二或第三周的课，她就在下课后来找我，说道，……
To answer your question, the youngest age at which I have seen a pupil propose a proof by contradiction to me was age eight. The girl had read some Life of Fred http://www.lifeoffredmath.com/ books for children about mathematics, and had newly joined my local mathematics class. On only the second or third week of class, she came up to me after class and said,…
……诸如此类。原教旨主义父母通常出奇地乐意让他们的孩子读这类书，因为它们完全是从圈内人的视角写出来的。《Fred 的生活》（Life of Fred）之所以受欢迎是有原因的。如果你想写一本关于科学理论和真理本质的书，尽管去写，但你根本无法对这部分特定的目标受众产生多大影响。
…and so on. Fundamentalist parents are often quite surprisingly happy for their children to read those kinds of books because they are written from the perspective of the in-group. There's a reason that Life of Fred is popular. If you want to write a book about the theory of science and what truth is, go ahead, but you aren't going to make much of an impact on that particular target audience.
我的孩子们分别是 13/11/9/7/3/1 岁，我们是在家自学（homeschool）。九月份新宝宝出生后，我接手了数学教学。我用《Fred 的生活》（Life of Fred）系列教最大的四个孩子。最小的那个刷书太快了，所以在圣诞节我给了她一个克里比奇棋盘（cribbage board），整个春天我们都在玩这个。她的加法水平很快就超过了9岁的老大，当我们玩起……
My kids are 13/11/9/7/3/1 and we homeschool. I took over math in September after the new baby came. I taught the four oldest from the Life of Fred series. The youngest was tearing through the books too fast, so at Christmas I gave her a cribbage board and we played that all spring. Her addition quickly surpassed the 9-year-old, and when we played…
《Fred 的生活》（Life of Fred）挺有意思的。不过你可能得把故事读给你儿子听。我大女儿最喜欢的《教学课本》（Teaching Textbooks）有视频辅导。《新加坡数学》（Singapore Math）也不错。还有一些程序你可以……
Life of Fred is pretty entertaining. Though you may need to read the stories to your son. Teaching Textbooks, my older daughter's favorite, has video tutoring. Singapore Math is good, too. There are programs you…
……另一个好玩的游戏是 Tiny Polka Dot——我们自己捣鼓出了超多不同的玩法。https://wordpress.com/posts/bancosparenting.wordpress.com 至于正经书，我们真的很喜欢《Fred 的生活》（Life of Fred）。https://www.rainbowresource.com/category/9813/Life-of-Fred.h...
…Another good game is Tiny Polka Dot - we've come up with so many of our own variations on the games. https://wordpress.com/posts/bancosparenting.wordpress.com In terms of actual books, we really enjoy Life of Fred. https://www.rainbowresource.com/category/9813/Life-of-Fred.h...
太神了！好书至关重要，对我的人生产生过塑造性的影响。学数学再加上《Fred 的生活》（Life of Fred），你就稳了。
Phenomenal! Good books are critical, and were formative to me. Add Life of Fred for math and you're golden.
为了回答你的问题，我见过提出反证法的学生里年龄最小的是八岁。那个小女孩读过几本关于数学的儿童读物《Fred 的生活》（Life of Fred，http://www.lifeoffredmath.com/），才刚加入我的本地数学班。才上了第二或第三周的课，她就在下课后来找我，说道，……
To answer your question, the youngest age at which I have seen a pupil propose a proof by contradiction to me was age eight. The girl had read some Life of Fred http://www.lifeoffredmath.com/ books for children about mathematics, and had newly joined my local mathematics class. On only the second or third week of class, she came up to me after class and said,…
……诸如此类。原教旨主义父母通常出奇地乐意让他们的孩子读这类书，因为它们完全是从圈内人的视角写出来的。《Fred 的生活》（Life of Fred）之所以受欢迎是有原因的。如果你想写一本关于科学理论和真理本质的书，尽管去写，但你根本无法对这部分特定的目标受众产生多大影响。
…and so on. Fundamentalist parents are often quite surprisingly happy for their children to read those kinds of books because they are written from the perspective of the in-group. There's a reason that Life of Fred is popular. If you want to write a book about the theory of science and what truth is, go ahead, but you aren't going to make much of an impact on that particular target audience.
我的孩子们分别是 13/11/9/7/3/1 岁，我们是在家自学（homeschool）。九月份新宝宝出生后，我接手了数学教学。我用《Fred 的生活》（Life of Fred）系列教最大的四个孩子。最小的那个刷书太快了，所以在圣诞节我给了她一个克里比奇棋盘（cribbage board），整个春天我们都在玩这个。她的加法水平很快就超过了9岁的老大，当我们玩起……
My kids are 13/11/9/7/3/1 and we homeschool. I took over math in September after the new baby came. I taught the four oldest from the Life of Fred series. The youngest was tearing through the books too fast, so at Christmas I gave her a cribbage board and we played that all spring. Her addition quickly surpassed the 9-year-old, and when we played…