Hi, im newbie of SQL user

Note: I use in MySQL
I attach sql script called testdb.sql
http://www.filefactory.com/file/cbe7a69/n/testdb.sql

I have 2 table which is product1,product2

Product1
PID ProductName ProductCode
1   Nike        N1
2   Adidas      A2
3   NewBalance  NB1
4   Puma        P3
.... etc

Product2
Date       PID
2009/1/14   1
2009/1/15   1
2009/2/1    2
2009/3/3    3
.........etc

Expected out is

ProductName Jan2009 Feb2009 Mar2009
 Adidas        1       1       0  
 NewBalance   30       0       1
 Nike          2       0       0   
 Puma         20       0       0

But, i tried wrote Nested Select statement query like this, the output is wrong :
select product1.ProductName ,
    (select count(product2.PID)
    from product1 as product1 left join product2 as product2
    on product1.pid=product2.pid
    and product2.pdate BETWEEN '2009/1/1' AND '2009/1/31')
    as 'Jan 2009',
   (select count(product2.PID)as 'Feb 2009'
    from product1 as product1 left join product2 as product2
    on product1.pid=product2.pid
    and product2.pdate BETWEEN '2009/2/1' AND '2009/2/28')as 'Feb 2009',
    (select count(product2.PID)
    from product1 as product1 left join product2 as product2
    on product1.pid=product2.pid
    and product2.pdate BETWEEN '2009/3/1' AND '2009/3/31') as 'Mar 2009'
    from product1 Group by product1.productName;



My output looks like this :(
ProductName Jan2009 Feb2009 Mar2009
 Nike         53      1       1  
 Adidas       53      1       1
 NewBalance   53      1       1   
 Puma         53      1       1


any solution ?

thanks
Regards
s1